Final answer:
The x-intercept of the line -5x + 9y = -18 is at (18/5, 0) by setting y to 0 and solving for x. The y-intercept is at (0, -2) by setting x to 0 and solving for y.
Step-by-step explanation:
To determine the intercepts of the line given by the equation -5x + 9y = -18, we need to find where the line crosses the x-axis and y-axis. This is done by setting one variable to zero and solving for the other.
Finding the x-intercept:
For the x-intercept, set y to 0:
-5x + 9(0) = -18
-5x = -18
x = 18/5
So, the x-intercept is (18/5, 0).
Finding the y-intercept:
For the y-intercept, set x to 0:
-5(0) + 9y = -18
9y = -18
y = -18/9
y = -2
So, the y-intercept is (0, -2).
The y-intercept represents the point at which the line crosses the y-axis, which is when x is zero.