Final answer:
Using the given points, the slope of the linear function h is determined to be -5. We then find the y-intercept to be 5, giving us the function h(x) = -5x + 5. Finally, we find that h(1) equals 0.
Step-by-step explanation:
To find a linear function h, we need to determine the slope (m) and y-intercept (b) of the function using the given points (9, -40) and (-2, 15). First, we calculate the slope:
m = (y2 - y1) / (x2 - x1) = (15 - (-40)) / (-2 - 9) = 55 / -11 = -5.
Now that we have the slope, we can use either point to find the y-intercept. Let's use the point (-2, 15):
15 = -5(-2) + b => 15 = 10 + b => b = 5.
The linear function is therefore h(x) = -5x + 5.
To find h(1), we substitute x with 1:
h(1) = -5(1) + 5 = -5 + 5 = 0.
The correct answer is h(x) = -5x + 5, and h(1) equals 0.