To find the equation of a linear function given two points (x₁, y₁) and (x₂, y₂), we can use the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept.
Given f(4) = -3 and f(0) = -2, we have two points: (4, -3) and (0, -2).
First, let's find the slope (m):
m = (y₂ - y₁) / (x₂ - x₁)
= (-2 - (-3)) / (0 - 4)
= 1 / (-4)
= -1/4
Now, let's substitute one of the points (0, -2) and the slope (-1/4) into the slope-intercept form to find the y-intercept (b):
-2 = (-1/4)(0) + b
-2 = 0 + b
b = -2
Therefore, the equation of the linear function f is:
f(x) = -1/4x - 2
Write a linear function f with f\left(4\right)=-3 and f\left(0\right)=-2
1 answer