### Home > AC > Chapter 7 > Lesson 7.3.3 > Problem7-105

7-105.

Find the equations of the lines described below.

1. The line parallel to the line $y=\frac{1}{5}x-6$ that goes through the point $\left(−5, 3\right)$.

Because the lines are parallel, they have the same slope.
Therefore, substitute the given $\left(x, y\right)$ coordinate into the equation for a line with the same slope as the equation above.

$y=\frac{1}{5}x-6 \rightarrow 3=\frac{1}{5}(-5)+b$

Now solve for b and rewrite the equation with $x$ and $y$ substituted back into their original positions.

$y=\frac{1}{5}x+4$

2. The line that goes through the points $\left(100, 76\right)$ and $\left(106, 58\right)$.

Make a slope triangle and find the differences in $x$ values and $y$ values to find the length of the legs of the triangle.
Use the values to find the slope.

Substitute one of the coordinates into the equation of a line, where $m = −3$, to solve for $b$.

Rewrite the equation with $x$ and $y$ substituted back into their original positions.