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=(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=(1)/(3)(-6)+b \\ 7=-2+b \\ 7+2=b \\ 9=b \end{gathered}`

Therefore, the equation is:

`y=(1)/(3)x+9`