Question

If F(4)=2 and F(3)=−1, what is the equation for F(x) in the form F(x)=ax+b?

a) F(x)=−x−9
b) F(x)=3x−11
c) F(x)=−2x+10
d) F(x)=4x−17

Answer 1

To find the equation for F(x), calculate the slope (a) using the change in y over change in x, and then solve for the y-intercept (b) using one of the given points. The correct equation is F(x) = 3x - 10.

Step-by-step explanation:

To find the equation for F(x) in the form F(x) = ax + b given that F(4) = 2 and F(3) = −1, you can use these two points to determine the slope (a) and then use either point to solve for the y-intercept (b).

The slope (a) is the change in y over the change in x, so:

a = ∆y / ∆x = (2 - (-1)) / (4 - 3) = 3/1 = 3

Now that we know a=3, we can substitute one of our points into the equation to find b. Using F(3) = −1:

−1 = 3(3) + b

b = −1 - 9 = −10

Therefore, the equation of F(x) is F(x) = 3x - 10, which matches with the option (c).