Question

write an equation in slope intercept form form for the line that passes through (-3,5) and is parallel to the graph of the line y=1/3x+4

Answer 1

If the line is parallel to

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

Then it has a slope of 1/3.

Using this slope, point (-3, 5) and the slope-point form,

$\begin{gathered} y-5=\frac{1}{3}(x+3) \\ \rightarrow y-5=\frac{1}{3}x+1 \end{gathered}$

Clearing y to get the slope-intercept form,

$\begin{gathered} y-5=\frac{1}{3}x+1 \\ \rightarrow y=\frac{1}{3}x+6 \end{gathered}$

We get that the equation of the line in slope-intercept form is:

$y=\frac{1}{3}x+6$