八年级数学上册一次函数知识点
\u516b\u5e74\u7ea7\u6570\u5b66\u4e0a\u518c\u51fd\u6570\u7684\u77e5\u8bc6\u70b9\u91cd\u70b9\uff1f\u5b9a\u4e49\u4e0e\u5b9a\u4e49\u5f0f\u3000\u3000\u81ea\u53d8\u91cfx\u548c\u56e0\u53d8\u91cfy\u6709\u5982\u4e0b\u5173\u7cfb\uff1a
\u3000\u3000y=kx \uff08k\u4e3a\u4efb\u610f\u4e0d\u4e3a\u96f6\u5b9e\u6570\uff09
\u3000\u3000\u6216y=kx+b \uff08k\u4e3a\u4efb\u610f\u4e0d\u4e3a\u96f6\u5b9e\u6570\uff0cb\u4e3a\u4efb\u610f\u5b9e\u6570\uff09
\u3000\u3000\u5219\u6b64\u65f6\u79f0y\u662fx\u7684\u4e00\u6b21\u51fd\u6570\u3002
\u3000\u3000\u7279\u522b\u7684\uff0c\u5f53b=0\u65f6\uff0cy\u662fx\u7684\u6b63\u6bd4\u4f8b\u51fd\u6570\u3002\u5373\uff1ay=kx \uff08k\u4e3a\u4efb\u610f\u4e0d\u4e3a\u96f6\u5b9e\u6570\uff09
\u3000\u3000\u6b63\u6bd4\u4f8b\u51fd\u6570\u56fe\u50cf\u7ecf\u8fc7\u539f\u70b9
\u3000\u3000\u5b9a\u4e49\u57df\uff1a\u81ea\u53d8\u91cf\u7684\u53d6\u503c\u8303\u56f4\uff0c\u81ea\u53d8\u91cf\u7684\u53d6\u503c\u5e94\u4f7f\u51fd\u6570\u6709\u610f\u4e49\uff1b\u8981\u4e0e\u5b9e\u9645\u76f8\u7b26\u5408\u3002
[\u7f16\u8f91\u672c\u6bb5]\u4e00\u6b21\u51fd\u6570\u7684\u6027\u8d28
\u3000\u30001.y\u7684\u53d8\u5316\u503c\u4e0e\u5bf9\u5e94\u7684x\u7684\u53d8\u5316\u503c\u6210\u6b63\u6bd4\u4f8b\uff0c\u6bd4\u503c\u4e3ak
\u3000\u3000\u5373\uff1ay=kx+b\uff08k\u22600) \uff08k\u4e0d\u7b49\u4e8e0\uff0c\u4e14k\uff0cb\u4e3a\u5e38\u6570\uff09
\u3000\u30002.\u5f53x=0\u65f6\uff0cb\u4e3a\u51fd\u6570\u5728y\u8f74\u4e0a\u7684,\u5750\u6807\u4e3a(0,b).
\u3000\u30003.k\u4e3a\u4e00\u6b21\u51fd\u6570y=kx+b\u7684\u659c\u7387,k=tan\u0398(\u89d2\u0398\u4e3a\u4e00\u6b21\u51fd\u6570\u56fe\u8c61\u4e0ex\u8f74\u6b63\u65b9\u5411\u5939\u89d2,\u0398\u226090\u00b0)
\u3000\u3000\u5f62\u3002\u53d6\u3002\u8c61\u3002\u4ea4\u3002\u51cf
\u3000\u30004.\u5f53b=0\u65f6\uff0c\u4e00\u6b21\u51fd\u6570\u56fe\u50cf\u53d8\u4e3a\u6b63\u6bd4\u4f8b\u51fd\u6570\uff0c\u6b63\u6bd4\u4f8b\u51fd\u6570\u662f\u7279\u6b8a\u7684\u4e00\u6b21\u51fd\u6570.
\u3000\u30005.\u51fd\u6570\u56fe\u50cf\u6027\u8d28\uff1a\u5f53k\u76f8\u540c\uff0c\u4e14b\u4e0d\u76f8\u7b49\uff0c\u56fe\u50cf\u5e73\u884c\uff1b\u5f53k\u4e0d\u540c\uff0c\u4e14b\u76f8\u7b49\uff0c\u56fe\u50cf\u76f8\u4ea4\uff1b\u5f53k\uff0cb\u90fd\u76f8\u540c\u65f6\uff0c\u4e24\u6761\u76f4\u7ebf\u91cd\u5408\u3002
[\u7f16\u8f91\u672c\u6bb5]\u4e00\u6b21\u51fd\u6570\u7684\u56fe\u50cf\u53ca\u6027\u8d28
\u3000\u30001\uff0e\u4f5c\u6cd5\u4e0e\u56fe\u5f62\uff1a\u901a\u8fc7\u5982\u4e0b3\u4e2a\u6b65\u9aa4
\u3000\u3000\uff081\uff09\u5217\u8868[\u4e00\u822c\u53d6\u4e24\u4e2a\u70b9,\u6839\u636e\u4e24\u70b9\u786e\u5b9a\u4e00\u6761\u76f4\u7ebf]\uff1b
\u3000\u3000\uff082\uff09\u63cf\u70b9\uff1b
\u3000\u3000\uff083\uff09\u8fde\u7ebf\uff0c\u53ef\u4ee5\u4f5c\u51fa\u4e00\u6b21\u51fd\u6570\u7684\u56fe\u50cf\u2014\u2014\u4e00\u6761\u76f4\u7ebf\u3002\u56e0\u6b64\uff0c\u4f5c\u4e00\u6b21\u51fd\u6570\u7684\u56fe\u50cf\u53ea\u9700\u77e5\u90532\u70b9\uff0c\u5e76\u8fde\u6210\u76f4\u7ebf\u5373\u53ef\u3002\uff08\u901a\u5e38\u627e\u51fd\u6570\u56fe\u50cf\u4e0ex\u8f74\u548cy\u8f74\u7684\u4ea4\u70b9\uff09
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\u3000\u30004\uff0ek\uff0cb\u4e0e\u51fd\u6570\u56fe\u50cf\u6240\u5728\u8c61\u9650\uff1a
\u3000\u3000y=kx\u65f6\uff08\u5373b\u7b49\u4e8e0\uff0cy\u4e0ex\u6210\u6b63\u6bd4)
\u3000\u3000\u5f53k\uff1e0\u65f6\uff0c\u76f4\u7ebf\u5fc5\u901a\u8fc7\u4e00\u3001\u4e09\u8c61\u9650\uff0cy\u968fx\u7684\u589e\u5927\u800c\u589e\u5927\uff1b
\u3000\u3000\u5f53k\uff1c0\u65f6\uff0c\u76f4\u7ebf\u5fc5\u901a\u8fc7\u4e8c\u3001\u56db\u8c61\u9650\uff0cy\u968fx\u7684\u589e\u5927\u800c\u51cf\u5c0f\u3002
\u3000\u3000y=kx+b\u65f6\uff1a
\u3000\u3000\u5f53 k>0,b>0, \u8fd9\u65f6\u6b64\u51fd\u6570\u7684\u56fe\u8c61\u7ecf\u8fc7\u4e00\uff0c\u4e8c\uff0c\u4e09\u8c61\u9650\u3002
\u3000\u3000\u5f53 k>0,b<0, \u8fd9\u65f6\u6b64\u51fd\u6570\u7684\u56fe\u8c61\u7ecf\u8fc7\u4e00\uff0c\u4e09\uff0c\u56db\u8c61\u9650\u3002
\u3000\u3000\u5f53 k0, \u8fd9\u65f6\u6b64\u51fd\u6570\u7684\u56fe\u8c61\u7ecf\u8fc7\u4e00\uff0c\u4e8c\uff0c\u56db\u8c61\u9650\u3002
\u3000\u3000\u5f53 k<0,b<0, \u8fd9\u65f6\u6b64\u51fd\u6570\u7684\u56fe\u8c61\u7ecf\u8fc7\u4e8c\uff0c\u4e09\uff0c\u56db\u8c61\u9650\u3002
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\u3000\u30004\u3001\u7279\u6b8a\u4f4d\u7f6e\u5173\u7cfb
\u3000\u3000\u5f53\u5e73\u9762\u76f4\u89d2\u5750\u6807\u7cfb\u4e2d\u4e24\u76f4\u7ebf\u5e73\u884c\u65f6\uff0c\u5176\u51fd\u6570\u89e3\u6790\u5f0f\u4e2dK\u503c\uff08\u5373\u4e00\u6b21\u9879\u7cfb\u6570\uff09\u76f8\u7b49
\u3000\u3000\u5f53\u5e73\u9762\u76f4\u89d2\u5750\u6807\u7cfb\u4e2d\u4e24\u76f4\u7ebf\u5782\u76f4\u65f6\uff0c\u5176\u51fd\u6570\u89e3\u6790\u5f0f\u4e2dK\u503c\u4e92\u4e3a\u8d1f\u5012\u6570\uff08\u5373\u4e24\u4e2aK\u503c\u7684\u4e58\u79ef\u4e3a-1\uff09
[\u7f16\u8f91\u672c\u6bb5]\u786e\u5b9a\u4e00\u6b21\u51fd\u6570\u7684\u8868\u8fbe\u5f0f
\u3000\u3000\u5df2\u77e5\u70b9A\uff08x1\uff0cy1\uff09\uff1bB\uff08x2\uff0cy2\uff09\uff0c\u8bf7\u786e\u5b9a\u8fc7\u70b9A\u3001B\u7684\u4e00\u6b21\u51fd\u6570\u7684\u8868\u8fbe\u5f0f\u3002
\u3000\u3000\uff081\uff09\u8bbe\u4e00\u6b21\u51fd\u6570\u7684\u8868\u8fbe\u5f0f\uff08\u4e5f\u53eb\u89e3\u6790\u5f0f\uff09\u4e3ay=kx+b\u3002
\u3000\u3000\uff082\uff09\u56e0\u4e3a\u5728\u4e00\u6b21\u51fd\u6570\u4e0a\u7684\u4efb\u610f\u4e00\u70b9P\uff08x\uff0cy\uff09\uff0c\u90fd\u6ee1\u8db3\u7b49\u5f0fy=kx+b\u3002\u6240\u4ee5\u53ef\u4ee5\u5217\u51fa2\u4e2a\u65b9\u7a0b\uff1ay1=kx1+b \u2026\u2026 \u2460 \u548c y2=kx2+b \u2026\u2026 \u2461
\u3000\u3000\uff083\uff09\u89e3\u8fd9\u4e2a\u4e8c\u5143\u4e00\u6b21\u65b9\u7a0b\uff0c\u5f97\u5230k\uff0cb\u7684\u503c\u3002
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[\u7f16\u8f91\u672c\u6bb5]\u4e00\u6b21\u51fd\u6570\u5728\u751f\u6d3b\u4e2d\u7684\u5e94\u7528
\u3000\u30001.\u5f53\u65f6\u95f4t\u4e00\u5b9a\uff0c\u8ddd\u79bbs\u662f\u901f\u5ea6v\u7684\u4e00\u6b21\u51fd\u6570\u3002s=vt\u3002
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[\u7f16\u8f91\u672c\u6bb5]\u5e38\u7528\u516c\u5f0f
\u3000\u30001.\u6c42\u51fd\u6570\u56fe\u50cf\u7684k\u503c\uff1a\uff08y1-y2)/(x1-x2)
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\u3000\u30003.\u6c42\u4e0ey\u8f74\u5e73\u884c\u7ebf\u6bb5\u7684\u4e2d\u70b9\uff1a|y1-y2|/2
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\u3000\u30006.\u6c42\u4efb\u610f2\u70b9\u6240\u8fde\u7ebf\u6bb5\u7684\u4e2d\u70b9\u5750\u6807\uff1a[\uff08x1+x2\uff09/2\uff0c\uff08y1+y2\uff09/2]
\u3000\u30007.\u6c42\u4efb\u610f2\u70b9\u7684\u8fde\u7ebf\u7684\u4e00\u6b21\u51fd\u6570\u89e3\u6790\u5f0f\uff1a\uff08X-x1\uff09/(x1-x2)=(Y-y1)/(y1-y2) (\u5176\u4e2d\u5206\u6bcd\u4e3a0\uff0c\u5219\u5206\u5b50\u4e3a0)
\u3000\u3000k b
\u3000\u3000+ + \u5728\u4e00\u8c61\u9650
\u3000\u3000+ - \u5728\u56db\u8c61\u9650
\u3000\u3000- + \u5728\u4e8c\u8c61\u9650
\u3000\u3000- - \u5728\u4e09\u8c61\u9650
\u3000\u30008.\u82e5\u4e24\u6761\u76f4\u7ebfy1=k1x+b1\u2225y2=k2x+b2\uff0c\u90a3\u4e48k1=k2\uff0cb1\u2260b2
\u3000\u30009.\u5982\u4e24\u6761\u76f4\u7ebfy1=k1x+b1\u22a5y2=k2x+b2\uff0c\u90a3\u4e48k1\u00d7k2=-1
\u3000\u300010.\u5de6\u79fbX\u5219B+X\uff0c\u53f3\u79fbX\u5219B-X
\u3000\u300011.\u4e0a\u79fbY\u5219X\u9879+Y\uff0c\u4e0b\u79fbY\u5219X\u9879-Y
\u3000\u3000(\u6709\u4e2a\u89c4\u5f8b.b\u9879\u7684\u503c\u7b49\u4e8ek\u4e58\u4e8e\u4e0a\u79fb\u7684\u5355\u4f4d\u5728\u51cf\u53bb\u539f\u6765\u7684b\u9879\u3002\uff09
\u3000\u3000\uff08\u6b64\u5904\u4e0d\u5168 \u613f\u6709\u4eba\u8865\u5145\uff09
\u3000\u3000\u4e0a\u79fb\uff1a(a\u4e3a\u79fb\u52a8\u7684\u6570\u91cf)Y=k\uff08X+a\uff09+b
\u3000\u3000Y=kX+ak+b
\u3000\u3000\u4e0b\u79fb\uff1a(a\u4e3a\u79fb\u52a8\u7684\u6570\u91cf)Y=k\uff08X-a\uff09+b
\u3000\u3000Y=kX-ak+xb
[\u7f16\u8f91\u672c\u6bb5]\u5e94\u7528
\u3000\u3000\u4e00\u6b21\u51fd\u6570y=kx+b\u7684\u6027\u8d28\u662f\uff1a\uff081\uff09\u5f53k>0\u65f6\uff0cy\u968fx\u7684\u589e\u5927\u800c\u589e\u5927\uff1b\uff082\uff09\u5f53k<0\u65f6\uff0cy\u968fx\u7684\u589e\u5927\u800c\u51cf\u5c0f\u3002\u5229\u7528\u4e00\u6b21\u51fd\u6570\u7684\u6027\u8d28\u53ef\u89e3\u51b3\u4e0b\u5217\u95ee\u9898\u3002
\u3000\u3000\u4e00\u3001\u786e\u5b9a\u5b57\u6bcd\u7cfb\u6570\u7684\u53d6\u503c\u8303\u56f4
\u3000\u3000\u4f8b1. \u5df2\u77e5\u6b63\u6bd4\u4f8b\u51fd\u6570 \uff0c\u5219\u5f53k<0\u65f6\uff0cy\u968fx\u7684\u589e\u5927\u800c\u51cf\u5c0f\u3002
\u3000\u3000\u89e3\uff1a\u6839\u636e\u6b63\u6bd4\u4f8b\u51fd\u6570\u7684\u5b9a\u4e49\u548c\u6027\u8d28\uff0c\u5f97 \u4e14m<0\uff0c\u5373 \u4e14 \uff0c\u6240\u4ee5 \u3002
\u3000\u3000\u4e8c\u3001\u6bd4\u8f83x\u503c\u6216y\u503c\u7684\u5927\u5c0f
\u3000\u3000\u4f8b2. \u5df2\u77e5\u70b9P1\uff08x1\uff0cy1\uff09\u3001P2\uff08x2\uff0cy2\uff09\u662f\u4e00\u6b21\u51fd\u6570y=3x+4\u7684\u56fe\u8c61\u4e0a\u7684\u4e24\u4e2a\u70b9\uff0c\u4e14y1>y2\uff0c\u5219x1\u4e0ex2\u7684\u5927\u5c0f\u5173\u7cfb\u662f\uff08 \uff09
\u3000\u3000A. x1>x2 B. x1<x2 C. x1=x2 D.\u65e0\u6cd5\u786e\u5b9a
\u3000\u3000\u89e3\uff1a\u6839\u636e\u9898\u610f\uff0c\u77e5k=3>0\uff0c\u4e14y1>y2\u3002\u6839\u636e\u4e00\u6b21\u51fd\u6570\u7684\u6027\u8d28\u201c\u5f53k>0\u65f6\uff0cy\u968fx\u7684\u589e\u5927\u800c\u589e\u5927\u201d\uff0c\u5f97x1>x2\u3002\u6545\u9009A\u3002
\u3000\u3000\u4e09\u3001\u5224\u65ad\u51fd\u6570\u56fe\u8c61\u7684\u4f4d\u7f6e
\u3000\u3000\u4f8b3. \u4e00\u6b21\u51fd\u6570y=kx+b\u6ee1\u8db3kb>0\uff0c\u4e14y\u968fx\u7684\u589e\u5927\u800c\u51cf\u5c0f\uff0c\u5219\u6b64\u51fd\u6570\u7684\u56fe\u8c61\u4e0d\u7ecf\u8fc7\uff08 \uff09
\u3000\u3000A. \u7b2c\u4e00\u8c61\u9650 B. \u7b2c\u4e8c\u8c61\u9650
\u3000\u3000C. \u7b2c\u4e09\u8c61\u9650 D. \u7b2c\u56db\u8c61\u9650
\u3000\u3000\u89e3\uff1a\u7531kb>0\uff0c\u77e5k\u3001b\u540c\u53f7\u3002\u56e0\u4e3ay\u968fx\u7684\u589e\u5927\u800c\u51cf\u5c0f\uff0c\u6240\u4ee5k<0\u3002\u6240\u4ee5b<0\u3002\u6545\u4e00\u6b21\u51fd\u6570y=kx+b\u7684\u56fe\u8c61\u7ecf\u8fc7\u7b2c\u4e8c\u3001\u4e09\u3001\u56db\u8c61\u9650\uff0c\u4e0d\u7ecf\u8fc7\u7b2c\u4e00\u8c61\u9650\u3002\u6545\u9009A . \u5178\u578b\u4f8b\u9898:
\u3000\u3000\u4f8b1. \u4e00\u4e2a\u5f39\u7c27\uff0c\u4e0d\u6302\u7269\u4f53\u65f6\u957f12cm,\u6302\u4e0a\u7269\u4f53\u540e\u4f1a\u4f38\u957f\uff0c\u4f38\u957f\u7684\u957f\u5ea6\u4e0e\u6240\u6302\u7269\u4f53\u7684\u8d28\u91cf\u6210\u6b63\u6bd4\u4f8b.\u5982\u679c\u6302\u4e0a3kg\u7269\u4f53\u540e\uff0c\u5f39\u7c27\u603b\u957f\u662f13.5cm\uff0c\u6c42\u5f39\u7c27\u603b\u957f\u662fy(cm)\u4e0e\u6240\u6302\u7269\u4f53\u8d28\u91cfx(kg)\u4e4b\u95f4\u7684\u51fd\u6570\u5173\u7cfb\u5f0f.\u5982\u679c\u5f39\u7c27\u6700\u5927\u603b\u957f\u4e3a23cm\uff0c\u6c42\u81ea\u53d8\u91cfx\u7684\u53d6\u503c\u8303\u56f4.
\u3000\u3000\u5206\u6790\uff1a\u6b64\u9898\u7531\u7269\u7406\u7684\u5b9a\u6027\u95ee\u9898\u8f6c\u5316\u4e3a\u6570\u5b66\u7684\u5b9a\u91cf\u95ee\u9898\uff0c\u540c\u65f6\u4e5f\u662f\u5b9e\u9645\u95ee\u9898\uff0c\u5176\u6838\u5fc3\u662f\u5f39\u7c27\u7684\u603b\u957f\u662f\u7a7a\u8f7d\u957f\u5ea6\u4e0e\u8d1f\u8f7d\u540e\u4f38\u957f\u7684\u957f\u5ea6\u4e4b\u548c\uff0c\u800c\u81ea\u53d8\u91cf\u7684\u53d6\u503c\u8303\u56f4\u5219\u53ef\u7531\u6700\u5927\u603b\u957f\u2192\u6700\u5927\u4f38\u957f\u2192\u6700\u5927\u8d28\u91cf\u53ca\u5b9e\u9645\u7684\u601d\u8def\u6765\u5904\u7406.
\u3000\u3000\u89e3\uff1a\u7531\u9898\u610f\u8bbe\u6240\u6c42\u51fd\u6570\u4e3ay=kx+12
\u3000\u3000\u521913.5=3k+12\uff0c\u5f97k=0.5
\u3000\u3000\u2234\u6240\u6c42\u51fd\u6570\u89e3\u6790\u5f0f\u4e3ay=0.5x+12
\u3000\u3000\u753123=0.5x+12\u5f97\uff1ax=22
\u3000\u3000\u2234\u81ea\u53d8\u91cfx\u7684\u53d6\u503c\u8303\u56f4\u662f0\u2264x\u226422
\u3000\u3000\u4f8b2
\u3000\u3000\u67d0\u5b66\u6821\u9700\u523b\u5f55\u4e00\u4e9b\u7535\u8111\u5149\u76d8\uff0c\u82e5\u5230\u7535\u8111\u516c\u53f8\u523b\u5f55\uff0c\u6bcf\u5f20\u97008\u5143\uff0c\u82e5\u5b66\u6821\u81ea\u523b\uff0c\u9664\u79df\u7528\u523b\u5f55\u673a120\u5143\u5916\uff0c\u6bcf\u5f20\u8fd8\u9700\u6210\u672c4\u5143\uff0c\u95ee\u8fd9\u4e9b\u5149\u76d8\u662f\u5230\u7535\u8111\u516c\u53f8\u523b\u5f55\uff0c\u8fd8\u662f\u5b66\u6821\u81ea\u5df1\u523b\u8d39\u7528\u8f83\u7701\uff1f
\u3000\u3000\u6b64\u9898\u8981\u8003\u8651X\u7684\u8303\u56f4
\u3000\u3000\u89e3:\u8bbe\u603b\u8d39\u7528\u4e3aY\u5143\uff0c\u523b\u5f55X\u5f20
\u3000\u3000\u7535\u8111\u516c\u53f8\uff1aY1=8X
\u3000\u3000\u5b66\u6821 \uff1aY2=4X+120
\u3000\u3000\u5f53X=30\u65f6\uff0cY1=Y2
\u3000\u3000\u5f53X>30\u65f6\uff0cY1>Y2
\u3000\u3000\u5f53X<30\u65f6\uff0cY1<Y2
\u3000\u3000\u3010\u8003\u70b9\u6307\u8981\u3011
\u3000\u3000\u4e00\u6b21\u51fd\u6570\u7684\u5b9a\u4e49\u3001\u56fe\u8c61\u548c\u6027\u8d28\u5728\u4e2d\u8003\u8bf4\u660e\u4e2d\u662fC\u7ea7\u77e5\u8bc6\u70b9\uff0c\u7279\u522b\u662f\u6839\u636e\u95ee\u9898\u4e2d\u7684\u6761\u4ef6\u6c42\u51fd\u6570\u89e3\u6790\u5f0f\u548c\u7528\u5f85\u5b9a\u7cfb\u6570\u6cd5\u6c42\u51fd\u6570\u89e3\u6790\u5f0f\u5728\u4e2d\u8003\u8bf4\u660e\u4e2d\u662fD\u7ea7\u77e5\u8bc6\u70b9.\u5b83\u5e38\u4e0e\u53cd\u6bd4\u4f8b\u51fd\u6570\u3001\u4e8c\u6b21\u51fd\u6570\u53ca\u65b9\u7a0b\u3001\u65b9\u7a0b\u7ec4\u3001\u4e0d\u7b49\u5f0f\u7efc\u5408\u5728\u4e00\u8d77\uff0c\u4ee5\u9009\u62e9\u9898\u3001\u586b\u7a7a\u9898\u3001\u89e3\u7b54\u9898\u7b49\u9898\u578b\u51fa\u73b0\u5728\u4e2d\u8003\u9898\u4e2d\uff0c\u5927\u7ea6\u5360\u67098\u5206\u5de6\u53f3.\u89e3\u51b3\u8fd9\u7c7b\u95ee\u9898\u5e38\u7528\u5230\u5206\u7c7b\u8ba8\u8bba\u3001\u6570\u5f62\u7ed3\u5408\u3001\u65b9\u7a0b\u548c\u8f6c\u5316\u7b49\u6570\u5b66\u601d\u60f3\u65b9\u6cd5.
\u3000\u3000\u4f8b2.\u5982\u679c\u4e00\u6b21\u51fd\u6570y=kx+b\u4e2dx\u7684\u53d6\u503c\u8303\u56f4\u662f-2\u2264x\u22646\uff0c\u76f8\u5e94\u7684\u51fd\u6570\u503c\u7684\u8303\u56f4\u662f-11\u2264y\u22649.\u6c42\u6b64\u51fd\u6570\u7684\u7684\u89e3\u6790\u5f0f\u3002
\u3000\u3000\u89e3\uff1a\uff081\uff09\u82e5k\uff1e0\uff0c\u5219\u53ef\u4ee5\u5217\u65b9\u7a0b\u7ec4 -2k+b=-11
\u3000\u30006k+b=9
\u3000\u3000\u89e3\u5f97k=2.5 b=-6 \uff0c\u5219\u6b64\u65f6\u7684\u51fd\u6570\u5173\u7cfb\u5f0f\u4e3ay=2.5x\u20146
\u3000\u3000\uff082\uff09\u82e5k\uff1c0\uff0c\u5219\u53ef\u4ee5\u5217\u65b9\u7a0b\u7ec4 -2k+b=9
\u3000\u30006k+b=-11
\u3000\u3000\u89e3\u5f97k=-2.5 b=4\uff0c\u5219\u6b64\u65f6\u7684\u51fd\u6570\u89e3\u6790\u5f0f\u4e3ay=-2.5x+4
\u3000\u3000\u3010\u8003\u70b9\u6307\u8981\u3011
\u3000\u3000\u6b64\u9898\u4e3b\u8981\u8003\u5bdf\u4e86\u5b66\u751f\u5bf9\u51fd\u6570\u6027\u8d28\u7684\u7406\u89e3\uff0c\u82e5k\uff1e0\uff0c\u5219y\u968fx\u7684\u589e\u5927\u800c\u589e\u5927\uff1b\u82e5k\uff1c0\uff0c\u5219y\u968fx\u7684\u589e\u5927\u800c\u51cf\u5c0f\u3002
\u3000\u3000\u4e00\u6b21\u51fd\u6570\u89e3\u6790\u5f0f\u7684\u51e0\u79cd\u7c7b\u578b
\u3000\u3000\u2460ax+by+c=0[\u4e00\u822c\u5f0f]
\u3000\u3000\u2461y=kx+b[\u659c\u622a\u5f0f]
\u3000\u3000\uff08k\u4e3a\u76f4\u7ebf\u659c\u7387\uff0cb\u4e3a\u76f4\u7ebf\u7eb5\u622a\u8ddd\uff0c\u6b63\u6bd4\u4f8b\u51fd\u6570b=0\uff09
\u3000\u3000\u2462y-y1=k(x-x1)[\u70b9\u659c\u5f0f]
\u3000\u3000\uff08k\u4e3a\u76f4\u7ebf\u659c\u7387,(x1,y1)\u4e3a\u8be5\u76f4\u7ebf\u6240\u8fc7\u7684\u4e00\u4e2a\u70b9\uff09
\u3000\u3000\u2463\uff08y-y1\uff09/(y2-y1)=(x-x1)/(x2-x1)[\u4e24\u70b9\u5f0f]
\u3000\u3000\uff08\uff08x1,y1\uff09\u4e0e\uff08x2,y2\uff09\u4e3a\u76f4\u7ebf\u4e0a\u7684\u4e24\u70b9\uff09
\u3000\u3000\u2464x/a-y/b=0[\u622a\u8ddd\u5f0f]
\u3000\u3000\uff08a\u3001b\u5206\u522b\u4e3a\u76f4\u7ebf\u5728x\u3001y\u8f74\u4e0a\u7684\u622a\u8ddd\uff09
\u3000\u3000\u89e3\u6790\u5f0f\u8868\u8fbe\u5c40\u9650\u6027\uff1a
\u3000\u3000\u2460\u6240\u9700\u6761\u4ef6\u8f83\u591a\uff083\u4e2a\uff09\uff1b
\u3000\u3000\u2461\u3001\u2462\u4e0d\u80fd\u8868\u8fbe\u6ca1\u6709\u659c\u7387\u7684\u76f4\u7ebf\uff08\u5e73\u884c\u4e8ex\u8f74\u7684\u76f4\u7ebf\uff09\uff1b
\u3000\u3000\u2463\u53c2\u6570\u8f83\u591a\uff0c\u8ba1\u7b97\u8fc7\u4e8e\u70e6\u7410\uff1b
\u3000\u3000\u2464\u4e0d\u80fd\u8868\u8fbe\u5e73\u884c\u4e8e\u5750\u6807\u8f74\u7684\u76f4\u7ebf\u548c\u8fc7\u5706\u70b9\u7684\u76f4\u7ebf\u3002
\u3000\u3000\u503e\u659c\u89d2\uff1ax\u8f74\u5230\u76f4\u7ebf\u7684\u89d2\uff08\u76f4\u7ebf\u4e0ex\u8f74\u6b63\u65b9\u5411\u6240\u6210\u7684\u89d2\uff09\u79f0\u4e3a\u76f4\u7ebf\u7684\u503e\u659c \u89d2\u3002\u8bbe\u4e00\u76f4\u7ebf\u7684\u503e\u659c\u89d2\u4e3aa\uff0c\u5219\u8be5\u76f4\u7ebf\u7684\u659c\u7387k=tg(a)
\u51fd\u6570y=kx+b(k,b\u4e3a\u5e38\u6570\uff0c\u4e14K\u4e0d\u7b49\u4e8e0\uff09\u4e3a\u4e00\u6b21\u51fd\u6570\u3002\u5f53b=0\u65f6\uff0c\u4e00\u6b21\u51fd\u6570y=kx+b\u5c31\u6210\u4e3ay=kx\uff08k\u4e3a\u5e38\u6570\uff0ck\u4e0d\u7b49\u4e8e0\uff09\u53eb\u505a\u6b63\u6bd4\u4f8b\u51fd\u6570\u3002
\u6ce8\u610f\uff1a1.\u81ea\u53d8\u91cfx\u7684\u4ee3\u6570\u5f0f\u662f\u6574\u5f0f
2.\u81ea\u53d8\u91cfx\u6b21\u6570\u662f1
3.\u81ea\u53d8\u91cfx\u7684\u7cfb\u6570k\u4e0d\u7b49\u4e8e0
\u8fd8\u6709\u5f88\u591a\uff0c\u6211\u60f3\u4f60\u6700\u597d\u53bb\u770b\u770b\u53c2\u8003\u4e66\uff0c\u4f1a\u66f4\u6e05\u695a
\u8bf7\u91c7\u7eb3\u3002
注意：1.自变量x的代数式是整式
2.自变量x次数是1
3.自变量x的系数k不等于0
还有很多，我想你最好去看看参考书，会更清楚
形如y=kx+b (k≠0）的函数为一次函数
y=kx+b
l,
绛旓細鍏勾绾т笂鍐屾暟瀛︿竴娆″嚱鏁扮煡璇1 鐭ヨ瘑鐐1 涓娆″嚱鏁板拰姝ｆ瘮渚嬪嚱鏁扮殑姒傚康 鑻ヤ袱涓彉閲弜锛寉闂寸殑鍏崇郴寮忓彲浠ヨ〃绀烘垚y=kx+b(k锛宐涓哄父鏁帮紝k鈮0)鐨勫舰寮锛屽垯绉皔鏄痻鐨勪竴娆″嚱鏁(x涓鸿嚜鍙橀噺)锛岀壒鍒湴锛屽綋b=0鏃讹紝绉皔鏄痻鐨勬姣斾緥鍑芥暟.鐭ヨ瘑鐐2 鍑芥暟鐨勫浘璞 鐢变簬涓ょ偣纭畾涓鏉＄洿绾匡紝涓鑸夊彇涓や釜鐗规畩鐐癸細鐩寸嚎涓巠杞...
绛旓細3銆佷竴娆″嚱鏁扮殑鍥捐薄(涓夋鐢诲浘璞)鐢变簬涓娆″嚱鏁皔=kx+b(k锛宐涓哄父鏁帮紝k鈮0)鐨勫浘璞℃槸涓鏉＄洿绾匡紝鎵浠ヤ竴娆″嚱鏁皔=kx+b鐨勫浘璞′篃绉颁负鐩寸嚎y=kx+b銆傜敱浜庝袱鐐圭‘瀹氫竴鏉＄洿绾匡紝鍥犳鍦ㄤ粖鍚庝綔涓娆″嚱鏁板浘璞℃椂锛屽彧瑕佹弿鍑洪傚悎鍏崇郴寮忕殑涓ょ偣锛屽啀杩炴垚鐩寸嚎鍗冲彲锛屼竴鑸夊彇涓や釜鐗规畩鐐:鐩寸嚎涓巠杞寸殑浜ょ偣(0锛宐)锛岀洿绾夸笌x杞...
绛旓細1.y鐨勫彉鍖栧间笌瀵瑰簲鐨剎鐨勫彉鍖栧兼垚姝ｆ瘮渚嬶紝姣斿间负k 鍗筹細y=kx+b (k涓轰换鎰忎笉涓洪浂鐨勫疄鏁 b鍙栦换浣曞疄鏁)2.褰搙=0鏃锛宐涓哄嚱鏁板湪y杞翠笂鐨勬埅璺濄備笁銆佷竴娆″嚱鏁扮殑鍥惧儚鍙婃ц川锛1.浣滄硶涓庡浘褰細閫氳繃濡備笅3涓楠 (1)鍒楄〃;(2)鎻忕偣;(3)杩炵嚎锛屽彲浠ヤ綔鍑轰竴娆″嚱鏁扮殑鍥惧儚--涓鏉＄洿绾裤傚洜姝わ紝浣滀竴娆″嚱鏁扮殑鍥惧儚鍙...
绛旓細鍩烘湰鏂规硶褰掔撼锛氬垽鏂竴涓嚱鏁版槸鍚︽槸涓娆″嚱鏁板叧閿槸鐪嬪畠鐨刱鏄惁涓嶄负0鍜岃嚜鍙橀噺鎸囨暟鏄惁涓1;鑰岃鍒ゆ柇鏄惁涓烘姣斾緥鍑芥暟杩樿鍦ㄤ竴娆″嚱鏁板熀纭涓婂姞涓奲=0杩欎釜鏉′欢銆2銆佷竴娆″嚱鏁扮殑鍥惧儚 鍩虹鐭ヨ瘑褰掔撼锛氭墍鏈変竴娆″嚱鏁扮殑鍥惧儚閮芥槸涓鏉＄洿绾匡紱涓娆″嚱鏁皔=kx锛媌鐨勫浘鍍忔槸缁忚繃鐐癸紙0,b锛夌殑鐩寸嚎銆傛姣斾緥鍑芥暟y=k/x鐨勫浘鍍忔槸缁...
绛旓細3銆佸畾涔夊煙锛氫竴鑸殑锛屼竴涓嚱鏁扮殑鑷彉閲忓厑璁稿彇鍊肩殑鑼冨洿锛屽彨鍋氳繖涓嚱鏁扮殑瀹氫箟鍩熴傚畾涔 涓娆″嚱鏁扮殑瀹氫箟锛氫竴鑸湴锛屽舰濡倅=kx+b锛坘锛宐鏄父鏁帮紝k鈮0锛夌殑鍑芥暟锛屽彨鍋氫竴娆″嚱鏁般傚嚱鏁扮殑鍥惧儚 涓鑸潵璇达紝瀵逛簬涓涓嚱鏁帮紝濡傛灉鎶婅嚜鍙橀噺涓庡嚱鏁扮殑姣忓瀵瑰簲鍊煎垎鍒綔涓虹偣鐨勬í銆佺旱鍧愭爣锛岄偅涔堝潗鏍囧钩闈㈠唴鐢辫繖浜涚偣缁勬垚鐨...
绛旓細2銆佹弿鐐癸細(鍦ㄧ洿瑙掑潗鏍囩郴涓紝浠ヨ嚜鍙橀噺鐨勫间负妯潗鏍囷紝鐩稿簲鐨鍑芥暟鍊间负绾靛潗鏍囷紝鎻忓嚭琛ㄦ牸涓暟鍊煎搴旂殑鍚勭偣銆3銆佽繛绾匡細(鎸夌収妯潗鏍囩敱灏忓埌澶х殑椤哄簭鎶婃墍鎻忕殑鍚勭偣鐢ㄥ钩婊戠殑鏇茬嚎杩炴帴璧锋潵)銆鐭ヨ瘑鐐鎬荤粨锛氬嚱鏁版湁涓夌琛ㄧず褰㈠紡(1)鍒楄〃娉 (2)鍥惧儚娉 (3)瑙ｆ瀽寮忔硶 骞抽潰鐩磋鍧愭爣绯 骞抽潰鐩磋鍧愭爣绯伙細 鍦ㄥ钩闈㈠唴鐢讳袱...
绛旓細7.姹備换鎰2鐐圭殑杩炵嚎鐨涓娆″嚱鏁瑙ｆ瀽寮忥細锛圶-x1锛/(x1-x2)=(Y-y1)/(y1-y2) (鍏朵腑鍒嗘瘝涓0锛屽垯鍒嗗瓙涓0)k b + + 鍦ㄤ竴璞￠檺 + - 鍦ㄥ洓璞￠檺 - + 鍦ㄤ簩璞￠檺 - - 鍦ㄤ笁璞￠檺 8.鑻ヤ袱鏉＄洿绾縴1=k1x+b1鈥杫2=k2x+b2锛岄偅涔坘1=k2锛宐1鈮燽2 9.濡備袱鏉＄洿绾縴1=k1x+b1鈯2=k2x+b2锛岄偅涔坘1...
绛旓細涓銆佺煡璇嗚鐐: 1銆佷竴娆″嚱鏁:鑻ヤ袱涓彉閲弜,y瀛樺湪鍏崇郴涓簓=kx+b (k鈮0, k,b涓哄父鏁)鐨勫舰寮,鍒欑Оy鏄痻鐨勫嚱鏁般 娉ㄦ剰:(1)k鈮0,鍚﹀垯鑷彉閲弜鐨勬渶楂樻椤圭殑绯绘暟涓嶄负1; (2)褰揵=0鏃,y=kx,y鍙玿鐨勬姣斾緥鍑芥暟銆 2銆佸浘璞:涓娆″嚱鏁扮殑鍥捐薄鏄竴鏉＄洿绾 (1)涓や釜甯告湁鐨勭壒娈婄偣:涓巠杞翠氦浜(0,b);涓巟杞翠氦浜(...
绛旓細1锛庝綔娉曚笌鍥惧舰锛氶氳繃濡備笅3涓楠 锛1锛夊垪琛紙2锛夋弿鐐癸紱3锛夎繛绾 2锛庢ц川锛氾紙1锛夊湪涓娆″嚱鏁颁笂鐨勪换鎰忎竴鐐筆锛坸锛寉锛夛紝閮芥弧瓒崇瓑寮忥細y=kx+b(k鈮0)銆傦紙2锛墆杞翠氦鐐圭殑鍧愭爣鎬绘槸锛0锛宐)锛屼笌x杞存绘槸浜や簬锛-b/k锛0锛夛紝姝ｆ瘮渚嬪嚱鏁扮殑鍥惧儚鎬绘槸杩囧師鐐广3锛巏锛宐涓庡嚱鏁板浘鍍忔墍鍦ㄨ薄闄愶細y=kx鏃 褰搆锛0...
绛旓細1 涓鑸湴锛屽舰濡倅=kx+b锛坘,b鏄父鏁帮紝k鈮0锛夌殑鍑芥暟鍙仛涓娆″嚱鏁銆2 鍏朵腑x鏄嚜鍙橀噺锛寉鏄洜鍙橀噺锛宬涓轰竴娆￠」绯绘暟锛寉鏄痻鐨勫嚱鏁般傚叾鍥捐薄涓轰竴鏉＄洿绾裤3 b=0鏃讹紝y=kx涓轰竴鏉￠氳繃鍘熺偣鐨勭洿绾裤傛槸姝ｆ瘮渚嬪嚱鏁般傚湪涓娆″嚱鏁皔=kx+b涓洜涓簒=0鏃讹紝y=0*k+b鍗硑=b锛屾墍浠 褰撶洿绾縴=kx+b鏈煡浣嗙粡杩噛杞...
