document.write( "Question 106865This question is from textbook intermediate algebra
\n" ); document.write( ": find the slope of the line that passes through (-3,1) and (2,-6).
\n" ); document.write( "find an equation of each line in standard form satisfying the given conditions. \n" ); document.write( "
Algebra.Com's Answer #77767 by MathLover1(20849)\"\" \"About 
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find the \"slope\" of the line that passes through (\"-3\",\"1\") and (\"2\",\"-6\").\r
\n" ); document.write( "\n" ); document.write( "\"slope+=+%28change_in_y%2Fchange_in_x%29\"\r
\n" ); document.write( "\n" ); document.write( "If \"slope+=+m\", \"change_in_y+=+y%5B2%5D+%96+y%5B1%5D\", \"change_in_x+=+x%5B2%5D+%96+x%5B1%5D\", then we have:\r
\n" ); document.write( "\n" ); document.write( "m =(y[2] – y[1])/(x[2] – x[1])\r
\n" ); document.write( "\n" ); document.write( "Since
\n" ); document.write( "\"x%5B1%5D+=-3\"
\n" ); document.write( "\"x%5B2%5D+=2\"
\n" ); document.write( "\"y%5B1%5D+=1\"
\n" ); document.write( "\"y%5B2%5D+=-6\"\r
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\n" ); document.write( "\n" ); document.write( "we will have:\r
\n" ); document.write( "\n" ); document.write( "m = (-6– 1)/(2 – (-3))\r
\n" ); document.write( "\n" ); document.write( "\"m+=+-7%2F%282+%2B+3%29\"\r
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\n" ); document.write( "\n" ); document.write( "\"m+=+-%287%2F5%29\"\r
\n" ); document.write( "\n" ); document.write( "We are trying to find equation \"y+=+ax+%2B+b\".
\n" ); document.write( "The value of slope \"a+=+-7%2F5\" is already given to us, as a point (\"-3\",\"1\") that lies on the line as well.\r
\n" ); document.write( "\n" ); document.write( "we need \"b\" which is:
\n" ); document.write( "\"b+=+y%5B1%5D\" – \"%28ax%5B1%5D%29\"\r
\n" ); document.write( "\n" ); document.write( "\"b+=+1+-+%28-7%2F5%28-3%29%29\"\r
\n" ); document.write( "\n" ); document.write( "\"b+=+1+-%2821%2F5%29\"
\n" ); document.write( "\"b+=+%285-21%29%2F5\"
\n" ); document.write( "\"b=+-%2816%2F5%29\"\r
\n" ); document.write( "\n" ); document.write( "so,
\n" ); document.write( "\"y+=+ax+%2B+b\" will be:\r
\n" ); document.write( "\n" ); document.write( "\"y+=+-%287%2F5%29x+-+16%2F5\" \r
\n" ); document.write( "\n" ); document.write( "here is the graph of this function, make sure that both given points (\"-3\",\"1\") and (\"2\",\"-6\")lie on line.\r
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Solved by pluggable solver: Graphing Linear Equations
In order to graph \"y=-1.4%2Ax-3.2\" we only need to plug in two points to draw the line
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\n" ); document.write( " So lets plug in some points
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\n" ); document.write( " Plug in x=-8
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\n" ); document.write( " \"y=-1.4%2A%28-8%29-3.2\"
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\n" ); document.write( " \"y=11.2-3.2\" Multiply
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\n" ); document.write( " \"y=8\" Add
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\n" ); document.write( " So here's one point (-8,8)
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\n" ); document.write( " Now lets find another point
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\n" ); document.write( " Plug in x=2
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\n" ); document.write( " \"y=-1.4%2A%282%29-3.2\"
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\n" ); document.write( " \"y=-2.8-3.2\" Multiply
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\n" ); document.write( " \"y=-6\" Add
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\n" ); document.write( " So here's another point (2,-6). Add this to our graph
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\n" ); document.write( " Now draw a line through these points
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\n" ); document.write( " So this is the graph of \"y=-1.4%2Ax-3.2\" through the points (-8,8) and (2,-6)
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\n" ); document.write( " So from the graph we can see that the slope is \"-1.4%2F1\" (which tells us that in order to go from point to point we have to start at one point and go down -1.4 units and to the right 1 units to get to the next point), the y-intercept is (0,\"-3.2\")and the x-intercept is (\"-2.28571428571429\",0)
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\n" ); document.write( " We could graph this equation another way. Since \"b=-3.2\" this tells us that the y-intercept (the point where the graph intersects with the y-axis) is (0,\"-3.2\").
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\n" ); document.write( " So we have one point (0,\"-3.2\")
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\n" ); document.write( " Now since the slope is \"-1.4%2F1\", this means that in order to go from point to point we can use the slope to do so. So starting at (0,\"-3.2\"), we can go down 1.4 units
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\n" ); document.write( " and to the right 1 units to get to our next point
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\n" ); document.write( " Now draw a line through those points to graph \"y=-1.4%2Ax-3.2\"
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\n" ); document.write( " So this is the graph of \"y=-1.4%2Ax-3.2\" through the points (0,-3.2) and (1,-4.6)
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