document.write( "Question 106069: Hello! Help
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\n" ); document.write( "\n" ); document.write( "Graph the linear equation using the slope and y-intercept.
\n" ); document.write( "1. y=1/5x+2\r
\n" ); document.write( "\n" ); document.write( "2. y=2x-3\r
\n" ); document.write( "\n" ); document.write( "3. y= -3/4x\r
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Algebra.Com's Answer #77166 by MathLover1(20849)\"\" \"About 
You can put this solution on YOUR website!
1. \"y=%281%2F5%29x%2B2\"\r
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Solved by pluggable solver: Graphing Linear Equations
In order to graph \"y=0.2%2Ax%2B2\" 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( "\n" ); document.write( "2. \"y=2x-3\"\r
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Solved by pluggable solver: Graphing Linear Equations
In order to graph \"y=2%2Ax-3\" 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=-3
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\n" ); document.write( " \"y=2%2A%28-3%29-3\"
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\n" ); document.write( " \"y=-6-3\" Multiply
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\n" ); document.write( " \"y=-9\" Add
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\n" ); document.write( " So here's one point (-3,-9)
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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=2%2A%28-2%29-3\"
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\n" ); document.write( " \"y=-4-3\" Multiply
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\n" ); document.write( " \"y=-7\" Add
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\n" ); document.write( " So here's another point (-2,-7). 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=2%2Ax-3\" through the points (-3,-9) and (-2,-7)
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\n" ); document.write( " So from the graph we can see that the slope is \"2%2F1\" (which tells us that in order to go from point to point we have to start at one point and go up 2 units and to the right 1 units to get to the next point) the y-intercept is (0,\"-3\")and the x-intercept is (\"1.5\",0) ,or (\"3%2F2\",0)
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\n" ); document.write( " We could graph this equation another way. Since \"b=-3\" this tells us that the y-intercept (the point where the graph intersects with the y-axis) is (0,\"-3\").
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\n" ); document.write( " So we have one point (0,\"-3\")
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\n" ); document.write( " Now since the slope is \"2%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\"), we can go up 2 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=2%2Ax-3\"
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\n" ); document.write( " So this is the graph of \"y=2%2Ax-3\" through the points (0,-3) and (1,-1)
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\n" ); document.write( "\n" ); document.write( "3. \"y=+%28-3%2F4%29x\"
\n" ); document.write( "Since, for some reason, the same way as previous two equations were solved doesn’t work for this one, we can find a solution for \"y=+%28-3%2F4%29x\"
\n" ); document.write( " by finding a line by slope and one point.\r
\n" ); document.write( "\n" ); document.write( "let point be (\"0\",\"0\") since \"b=0\" and
\n" ); document.write( "slope \"-%283%2F4%29\"\r
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Solved by pluggable solver: FIND a line by slope and one point

\n" ); document.write( " What we know about the line whose equation we are trying to find out:
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  • it goes through point (0, 0)

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  • it has a slope of -0.75

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\n" ); document.write( " First, let's draw a diagram of the coordinate system with point (0, 0) plotted with a little blue dot:
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\n" ); document.write( " Write this down: the formula for the equation, given point \"x%5B1%5D%2C+y%5B1%5D\" and intercept a, is
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\n" ); document.write( " \"y=ax+%2B+%28y%5B1%5D-a%2Ax%5B1%5D%29\" (see a paragraph below explaining why this formula is correct)
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\n" ); document.write( " Given that a=-0.75, and \"system%28+x%5B1%5D+=+0%2C+y%5B1%5D+=+0+%29+\", we have the equation of the line:
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\n" ); document.write( " \"y=-0.75%2Ax+%2B+0\"
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\n" ); document.write( " Explanation: Why did we use formula \"y=ax+%2B+%28y%5B1%5D+-+a%2Ax%5B1%5D%29\" ? Explanation goes here. We are trying to find equation y=ax+b. The value of slope (a) is already given to us. We need to find b. If a point (\"x%5B1%5D\", \"y%5B1%5D\") lies on the line, it means that it satisfies the equation of the line. So, our equation holds for (\"x%5B1%5D\", \"y%5B1%5D\"): \"y%5B1%5D+=+a%2Ax%5B1%5D%2Bb\" Here, we know a, \"x%5B1%5D\", and \"y%5B1%5D\", and do not know b. It is easy to find out: \"b=y%5B1%5D-a%2Ax%5B1%5D\". So, then, the equation of the line is: \"+y=ax%2B%28y%5B1%5D-a%2Ax%5B1%5D%29+\".
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\n" ); document.write( " Here's the graph:
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