Final answer:
To find the linear function h with given values, we use the formula y = mx + b. A slope and a point are used to find the values for m and b. Substituting x = 4 into the equation will give the value of h(4).
Step-by-step explanation:
To find the linear function h, we can use the formula y = mx + b, where m is the slope and b is the y-intercept. We are given two points: (9, -31) and (-1, 9). We can use these points to find the values of m and b.
Let's first find the slope, m. We can use the formula m = (y2 - y1) / (x2 - x1). Plugging in the values, we get m = (9 - (-31)) / (-1 - 9) = (9 + 31) / (-10) = 40 / (-10) = -4.
Next, we can choose one of the points to find the y-intercept, b. Let's use the point (9, -31) and substitute the values into the equation y = mx + b. We have -31 = -4(9) + b. Solving for b, we get b = -31 + 36 = 5.
So the linear function h is y = -4x + 5. To find h(4), we substitute x = 4 into the equation. h(4) = -4(4) + 5 = -16 + 5 = -11.