Question

What is the function rule for the line? O f(x) = - 3/2 * x + 2 Of f(x) = - 3/2 * x - 2 Of f(x) = 3/2 * x - 2 O f(x) = - 2/3 * x - 2

Answer 1

The function rule of the line is f(x) = -
`(3)/(2)` x - 2 ⇒ 2nd answer

Explanation:

* Let us make the equation of the line

- The slope of a line m =
`(y_(2)-y_(1))/(x_(2)-x_(1))`, where

`(x_(1),y_(1))` and
`(x_(2),y_(2))` are two points lie on the line

- The form of the equation of a line is y = mx + c, where m is the slope

of the line and c is the y-intercept

- From the attached figure

∵ The line passes through points (0 , -2) and (-2 , 1)

∴ m =
`(1-(-2))/((-2)-0)=(1+2)/(-2)=-(3)/(2)`

∵ y = mx + c

- The line intersects y-axis at -2

∴ c = -2

∴ y = -
`(3)/(2)` x + (-2)

∴ y = -
`(3)/(2)` x - 2

∵ y = f(x)

∴ f(x) = -
`(3)/(2)` x - 2

* The function rule of the line is f(x) = -
`(3)/(2)` x - 2