Answer:
y = 1/3x + 1
Explanation:
The equation of a line with slope m that passes through the point (x1, y1) can be founded using the following:
[tex]y-y_1=m(x-x_1)[/tex]If the line is parallel to y = 1/3x - 5, the line will have the same slope. Since the slope of y = 1/3x - 5 is 1/3 because it is the value beside the x, the slope of our line is also 1/3
Then, replacing m by 1/3 and (x1, y1) by (3, 2), we get:
[tex]y-2=\frac{1}{3}(x-3)[/tex]Finally, solve for y:
[tex]\begin{gathered} y-2=\frac{1}{3}(x)-\frac{1}{3}(3) \\ y-2=\frac{1}{3}x-1 \\ y-2+2=\frac{1}{3}x-1+2 \\ y=\frac{1}{3}x+1 \end{gathered}[/tex]Therefore, the equation of the line is:
y = 1/3x + 1
