Write a linear function f with the values f(10) = 5 and f (2)=-3

Answer 1

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