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Find a linear function h, given h(9) = –40 and h( -2) = 15. Then find h(1).

a) h(x) = 5x - 5
b) h(x) = -5x + 5
c) h(x) = -5x - 5
d) h(x) = 5x + 5

User TitoOrt
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1 Answer

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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.

User Steven Mark Ford
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