what would be an equation of a line that passes through (3,2) and has the same x-intercept as y=2x-12

Start by finding the x intercept of y=2x-12

To find the x intercept, set y = 0
0 = 2x - 12
x = 6

Now you have the points (3, 2) and (0, 6). Find the slope.

(2-6)/(3-0) = -4/3

Use y - y1 = m(x - x1) to find the equation of the line.

y - 0 = -4/3(x - 3)
y = -4/3x + 4