document.write( "Question 686685: i need the answer for the following & steps:(-1,0),b=3
\n" ); document.write( "m=-2,(3,-7)
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Algebra.Com's Answer #424888 by KMST(5328) $\"\"$ $\"About$

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In the x-y plane, the equation of a line that is not \"vertical\" can be written, in the $\"highlight%28slope-intercept%29\"$ form, as $\"highlight%28y=mx%2Bb%29\"$
\n" ); document.write( "The number $\"m\"$ is the $\"highlight%28slope%29\"$ , and $\"b\"$ is the $\"highlight%28y-intercept%29\"$ .
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\n" ); document.write( "PROBLEM # 1
\n" ); document.write( "If a line passes through the point (-1,0) and has the y-intercept $\"b=3\"$ ,
\n" ); document.write( "its equation will be $\"y=mx%2B3\"$
\n" ); document.write( "We just have to find $\"m\"$ .
\n" ); document.write( "THE SIMPLE WAY:
\n" ); document.write( "We know that the point (-1,0), with $\"x=-1\"$ and $\"y=0\"$
\n" ); document.write( "belongs to that line, so we substitute those values for $\"x\"$ and $\"y\"$ tp get
\n" ); document.write( " $\"0=m%28-1%29%2B3\"$ --> $\"0=-m%2B3\"$ --> $\"highlight%28m=3%29\"$
\n" ); document.write( "The equation for that line is $\"y=mx%2Bb\"$ with $\"m=3\"$ and $\"b=3\"$ , so it is $\"highlight%28y=3x%2B3%29\"$
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\n" ); document.write( "PROBLEM # 2
\n" ); document.write( "If a line has a slope of $\"m=-2\"$ ,
\n" ); document.write( "and passes through the point (3,-7), with $\"x=3\"$ and $\"y=-7\"$ ,
\n" ); document.write( "the equation of the line in slope-intercept form will be $\"y=-2x%2Bb\"$ with some $\"b\"$ .
\n" ); document.write( "ONE WAY:
\n" ); document.write( "We can find $\"b\"$ by substituting the coordinates of the point (3,-7) given
\n" ); document.write( " $\"-7=-2%283%29%2Bb\"$ --> $\"-7=-6%2Bb\"$ --> $\"-7%2B6=-6%2Bb%2B6\"$ --> $\"-1=b\"$
\n" ); document.write( "So the equation is $\"highlight%28y=-2x-1%29\"$
\n" ); document.write( "ANOTHER WAY:
\n" ); document.write( "The equation of a line with slope $\"m\"$ .
\n" ); document.write( "that passes through point P( $\"x%5BP%5D\"$ , $\"y%5BP%5D\"$ ) is
\n" ); document.write( " $\"highlight%28y-y%5BP%5D=m%28x-x%5BP%5D%29%29\"$ in $\"highlight%28point-slope%29\"$ form
\n" ); document.write( "Substituting the coordinates of our point P(3,-7),
\n" ); document.write( "and $\"m=-2\"$
\n" ); document.write( "we get
\n" ); document.write( " $\"y-%28-7%29=-2%28x-3%29\"$ --> $\"y%2B7=-2x%2B6\"$ --> $\"y=-2x%2B6-7\"$ --> $\"highlight%28y=-2x-1%29\"$
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