Final answer:
To determine the intercepts of the line given by the equation y - 4 = 7(x - 6), we find the x-intercept by setting y = 0 and solving for x, and the y-intercept by setting x = 0 and solving for y.
Step-by-step explanation:
To determine the intercepts of the line given by the equation y - 4 = 7(x - 6), we need to find the x-intercept and the y-intercept. The x-intercept is the point at which the line crosses the x-axis, and the y-coordinate is 0. To find it, we can set y = 0 and solve for x: 0 - 4 = 7(x - 6).
0 - 4 = 7x - 42
7x = 38
x = 38/7.
So the x-intercept is (38/7, 0).
The y-intercept is the point at which the line crosses the y-axis, and the x-coordinate is 0. To find it, we can set x = 0 and solve for y: y - 4 = 7(0 - 6).
y - 4 = -42
y = -42 + 4 = -38.
So the y-intercept is (0, -38).