Answer:
y=1/3x+1
Explanation:
Two lines are parallel if they have the same slope.
Comparing the equation of the line with the slope-intercept form:
[tex]\begin{gathered} y=mx+b \\ y=\frac{1}{3}x-5 \\ \implies\text{Slope, m}=\frac{1}{3} \end{gathered}[/tex]Therefore, the line parallel to it has a slope of 1/3.
Thus, using the slope-point form, we find the equation of a line with a slope of 1/3 and passing through (3,2).
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-2=\frac{1}{3}(x-3) \\ y-2=\frac{1}{3}x-1 \\ y=\frac{1}{3}x-1+2 \\ y=\frac{1}{3}x+1 \end{gathered}[/tex]The equation of the parallel line is y=1/3x+1.
