Equation of a line with a slope of 1/4 and an x-intercept of 8

First, we can start with the equation of a line

y = mx + b

We are given the slope, m = 1/4. Plug this into our function

y = 1/4 x + b

Now we need to find b (y-intercept). We are given the x-intercept, where the line crosses the x-axis. So we know the value of y = 0 at the x-intercept. This point is (8,0). We can plug this value into our equation above (since we know this point is on the line) and solve for b.

0 = 1/4(8) + b
0 = 2 + b
b = -2

Plug this b value into the equation we were building for our final equation

y = 1/4 x - 2