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

Answer:

The function rule of the line is f(x) = - $\frac{3}{2}$ x - 2 ⇒ 2nd answer

Step-by-step explanation:

* Let us make the equation of the line

- The slope of a line m = $\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$, 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 = $\frac{1-(-2)}{(-2)-0}=\frac{1+2}{-2}=-\frac{3}{2}$

∵ y = mx + c

- The line intersects y-axis at -2

∴ c = -2

∴ y = -$\frac{3}{2}$ x + (-2)

∴ y = - $\frac{3}{2}$ x - 2

∵ y = f(x)

∴ f(x) = - $\frac{3}{2}$ x - 2

* The function rule of the line is f(x) = - $\frac{3}{2}$ x - 2