Question

Need help with homework

Answer 1

So,

First of all, remember that two lines are parallel when their slopes are equal.

We want to find an equation of the line passing through the point (-6,7) that is parallel to the line:

$y=\frac{1}{3}x+4$

For this, first remember that any line has the following main form:

$y=mx+b$

Where "m" is the slope and "b" is the y-intercept.

Given that the line that we want to find is parallel, its slope is 1/3.

So, what we're going to do is to replace the point (x,y) = (-6,7) and the slope m = 1/3 in the main equation to find the value of b and then replace.

This is:

$\begin{gathered} 7=\frac{1}{3}(-6)+b \\ 7=-2+b \\ 7+2=b \\ 9=b \end{gathered}$

Therefore, the equation is:

$y=\frac{1}{3}x+9$