Question
Write a linear function f with the values f(10) = 5 and f (2)=-3
Answers
Answered by
GPT 3.5
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
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