In the linear function h, h(0) = 41 and h(1) = 40.Which equation defines h ?A) h(x) = −x + 41B) h(x) = −xC) h(x) = −41xD) h(x) = −41
Question
In the linear function h, h(0) = 41 and h(1) = 40.
Which equation defines h ?
A) h(x) = −x + 41
B) h(x) = −x
C) h(x) = −41x
D) h(x) = −41
Solution
The correct equation that defines h is A) h(x) = -x + 41.
Here's why:
A linear function is defined as h(x) = mx + b, where m is the slope and b is the y-intercept.
Given that h(0) = 41, we can substitute x = 0 into the equation to find the y-intercept (b). This gives us h(0) = m*0 + b, which simplifies to b = 41.
Next, we know that h(1) = 40. We can substitute x = 1 and b = 41 into the equation to find the slope (m). This gives us 40 = m*1 + 41, which simplifies to m = -1.
Therefore, the equation that defines h is h(x) = -x + 41.
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