document.write( "Question 102158: Hello I am having trouble in finding slope and intercept forms and I need help on some problems:
\n" ); document.write( "1. Find the slope and y-intercept of y-6= -2x AND y= x+2\r
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\n" ); document.write( "(-3,-2),(4,-2)
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Algebra.Com's Answer #74234 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
\"Find the slope and y-intercept of y-6= -2x\"\r
\n" ); document.write( "\n" ); document.write( "\"y-6=+-2x+\" Start with the given equation\r
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\n" ); document.write( "\n" ); document.write( "\"y=+-2x%2B6+\" Add 6 to both sides. So the equation is in slope intercept form \"y=mx%2Bb\" where the slope is \"m=-2\" and the y-intercept is \"b=6\"\r
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\n" ); document.write( "\n" ); document.write( "\"Find the slope and y-intercept of y= x+2\"\r
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\n" ); document.write( "\n" ); document.write( "Since \"y=+x%2B2+\" is in slope intercept form \"y=mx%2Bb\", the slope is m=1 (remember it really looks like \"y=1%2Ax%2B2\") and the y-intercept is b=2\r
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\n" ); document.write( "\n" ); document.write( "\"Find the slope of the line that passes through each pair of points:
\n" ); document.write( "(-3,-2),(4,-2)\"\r
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Solved by pluggable solver: Finding the Equation of a Line
First lets find the slope through the points (\"-3\",\"-2\") and (\"4\",\"-2\")
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\n" ); document.write( " \"m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29\" Start with the slope formula (note: (\"x%5B1%5D\",\"y%5B1%5D\") is the first point (\"-3\",\"-2\") and (\"x%5B2%5D\",\"y%5B2%5D\") is the second point (\"4\",\"-2\"))
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\n" ); document.write( " \"m=%28-2--2%29%2F%284--3%29\" Plug in \"y%5B2%5D=-2\",\"y%5B1%5D=-2\",\"x%5B2%5D=4\",\"x%5B1%5D=-3\" (these are the coordinates of given points)
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\n" ); document.write( " \"m=+0%2F7\" Subtract the terms in the numerator \"-2--2\" to get \"0\". Subtract the terms in the denominator \"4--3\" to get \"7\"
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\n" ); document.write( " \"m=0\" Reduce
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\n" ); document.write( " So the slope is
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\n" ); document.write( " \"m=0\"
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\n" ); document.write( "Now let's use the point-slope formula to find the equation of the line:
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\n" ); document.write( " ------Point-Slope Formula------
\n" ); document.write( " \"y-y%5B1%5D=m%28x-x%5B1%5D%29\" where \"m\" is the slope, and (\"x%5B1%5D\",\"y%5B1%5D\") is one of the given points
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\n" ); document.write( " So lets use the Point-Slope Formula to find the equation of the line
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\n" ); document.write( " \"y--2=%280%29%28x--3%29\" Plug in \"m=0\", \"x%5B1%5D=-3\", and \"y%5B1%5D=-2\" (these values are given)
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\n" ); document.write( " \"y%2B2=%280%29%28x--3%29\" Rewrite \"y--2\" as \"y%2B2\"
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\n" ); document.write( " \"y%2B2=%280%29%28x%2B3%29\" Rewrite \"x--3\" as \"x%2B3\"
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\n" ); document.write( " \"y%2B2=0x%2B%280%29%283%29\" Distribute \"0\"
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\n" ); document.write( " \"y%2B2=0x%2B0\" Multiply \"0\" and \"3\" to get \"0%2F0\". Now reduce \"0%2F0\" to get \"0\"
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\n" ); document.write( " \"y=0x%2B0-2\" Subtract \"2\" from both sides to isolate y
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\n" ); document.write( " \"y=0x-2\" Combine like terms \"0\" and \"-2\" to get \"-2\"
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\n" ); document.write( " So the equation of the line which goes through the points (\"-3\",\"-2\") and (\"4\",\"-2\") is:\"y=0x-2\"
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\n" ); document.write( " The equation is now in \"y=mx%2Bb\" form (which is slope-intercept form) where the slope is \"m=0\" and the y-intercept is \"b=-2\"
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\n" ); document.write( " Notice if we graph the equation \"y=0x-2\" and plot the points (\"-3\",\"-2\") and (\"4\",\"-2\"), we get this: (note: if you need help with graphing, check out this solver)
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\n" ); document.write( " Graph of \"y=0x-2\" through the points (\"-3\",\"-2\") and (\"4\",\"-2\")
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\n" ); document.write( " Notice how the two points lie on the line. This graphically verifies our answer.
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\n" ); document.write( "\n" ); document.write( "So \"y=0x-2\" then becomes \"y=-2\", which is the equation of the line through the points (-3,-2),(4,-2)
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