The linear function f i with values f(-1) = 10 and f(5) = -1 is f(x)

Use the two points to compute the slope, m, then use one of the points in the form y=m(x)+b to find the value of b.

The equation for the slope, m, of a line is:

m=y1−y0x1−x0 [1]

The equation f(2)=−1 tells us that x0=2andy0=−1; substitute this into equation [1]:

m=y1−−1x1−2 [2]

The equation f(5)=4 tells us that x1=5andy1=4; substitute this into equation [2]:

m=4−−15−2 [3]

m=53

Substitute 53 for m into the equation y=m(x)+b

y=53x+b [4]

Substitute 2 for x and -1 for y and the solve for b:

−1=53(2)+b

b=−133

Substitute −133 for b in equation [4]:

y=53x−133 [5]

Check:

−1=53(2)−133
4=53(5)−133

−1=−1
4=4

Hope this helps