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

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

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Guest Sep 21, 2017

#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
+1811
+2

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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