Final answer:
To find the intercepts of the equation -5x - 4y = 10, you set x to 0 to find the y-intercept, which is (0, -2.5), and set y to 0 to find the x-intercept, which is (-2, 0).
Step-by-step explanation:
Determining the Intercepts of a Line
To find the intercepts of the line given by the equation -5x - 4y = 10, we need to find the points where the line crosses the x-axis and the y-axis. These are called the x-intercept and the y-intercept, respectively.
Finding the y-intercept
To find the y-intercept, set x to zero and solve for y. Plugging in 0 for x gives us:
-5(0) - 4y = 10
=> -4y = 10
=> y = -2.5
So the y-intercept is (0, -2.5).
Finding the x-intercept
To find the x-intercept, set y to zero and solve for x. Plugging in 0 for y gives us:
-5x - 4(0) = 10
=> -5x = 10
=> x = -2
So the x-intercept is (-2, 0).