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through: (-4,0), parallel to y=3/4x-2 

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Guest Sep 21, 2017

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 #1
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To find the equation that passes through \((-4,0)\) and is parallel to the line \(y=\frac{3}{4}x-2\), we must understand a few properties. 

 

1) Parallel lines have the same slope.

 

This fact, alone, can help us do half the problem. The slope of the line \(y=\frac{3}{4}x-2\) is \(\frac{3}{4}\). As I stated above, parallel lines have the same slope, so the equation of this unknown line is \(\frac{3}{4}\).

 

We have deduced already that this unknown line is in the form of \(y=\frac{3}{4}x+b \). The only thing to find now is the b:
 

\(y=\frac{3}{4}x+b \) Now, plug in a coordinate that we know is on the line. In this case, we only know that \((-4,0)\) lies on the line. Plug it in for x and y.
\(0=\frac{3}{4}*\frac{-4}{1}+b\) Simplif the right hand side.
\(0=-3+b\) Add 3 to both sides of the equation.
\(b=3\)  
   

 

We have found both of the mystery values to construct the proper equation of a line. It is \(y=\frac{3}{4}x+3\)

TheXSquaredFactor  Sep 21, 2017
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1+0 Answers

 #1
avatar+1221 
+2
Best Answer

To find the equation that passes through \((-4,0)\) and is parallel to the line \(y=\frac{3}{4}x-2\), we must understand a few properties. 

 

1) Parallel lines have the same slope.

 

This fact, alone, can help us do half the problem. The slope of the line \(y=\frac{3}{4}x-2\) is \(\frac{3}{4}\). As I stated above, parallel lines have the same slope, so the equation of this unknown line is \(\frac{3}{4}\).

 

We have deduced already that this unknown line is in the form of \(y=\frac{3}{4}x+b \). The only thing to find now is the b:
 

\(y=\frac{3}{4}x+b \) Now, plug in a coordinate that we know is on the line. In this case, we only know that \((-4,0)\) lies on the line. Plug it in for x and y.
\(0=\frac{3}{4}*\frac{-4}{1}+b\) Simplif the right hand side.
\(0=-3+b\) Add 3 to both sides of the equation.
\(b=3\)  
   

 

We have found both of the mystery values to construct the proper equation of a line. It is \(y=\frac{3}{4}x+3\)

TheXSquaredFactor  Sep 21, 2017

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