f(0)=-5,f(4)=-3

Question

write a linear function f with the given values

Answer 1

Hello, thank you for taking the time to post your question!

The general form that we’re after here is y = mx + b, but in order to get it in that form we need to find both the slope(m) and y-intercept(b) values with the points given. For the points given that means

m = (y2 – y1) / (x2 – x1) = (-3 - -5) / (4 – 0) = 2/4 = 1/2

Then b = -5 since one of the points given is the y-intercept (0, -5)

Putting it all together makes the equation y = 1/2x - 5

I hope that helps get you moving in the right direction! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

Since f(0) = -5 and f(4) = -3, the points (0, -5) and (4, -3) are points on the line.

Slope = (-3 - (-5)) / (4 - 0) = 1/2

Equation of line y - (-5) = (1/2)(x - 0)

y = (1/2)x - 5

y = f(x) = (1/2)x - 5