To find the equation of the linear function f, we need to first determine the slope of the line passing through the two given points (10, 5) and (2, -3).
The formula for the slope of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by:
m = (y₂ - y₁) / (x₂ - x₁)
Using the coordinates (10, 5) and (2, -3), we can calculate the slope:
m = (-3 - 5) / (2 - 10)
m = -8 / (-8)
m = 1
Now that we have the slope, we can use the point-slope form of a linear equation to find the value of f(x):
y - y₁ = m(x - x₁)
Plugging in the point (10, 5), we get:
y - 5 = 1(x - 10)
y - 5 = x - 10
y = x - 5
Therefore, the linear function f is:
f(x) = x - 5
Write a linear function f with the values f(10) = 5 and f (2)=-3
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