Final answer:
To find the x-intercept of the line y = -1/4x + 2, y is set to zero, and the resulting equation is solved for x, which gives an x-intercept of 8.
Step-by-step explanation:
The x-intercept of a line in the (x, y) coordinate plane is the point at which the line crosses the x-axis. To find the x-intercept of the line y = -1/4x + 2, we set y to 0 (since at any point on the x-axis, the y-coordinate is 0) and solve for x:
0 = -1/4x + 2
Multiplying both sides by -4 to get rid of the fraction:
0 = x - 8
Adding 8 to both sides:
8 = x
Thus, the x-intercept of the line is 8 (or at the point (8, 0) on the coordinate plane).