Question

What is the rate of change of the linear relationship modeled in the table (-2,5) (-1,4) (0,3) (1,2)

Answer 1

The rate of change of the linear relationship is -1.

Explanation:

It is given that there is a linear relationship between all these points, these points lie on a straight line.

The equation to find the slope passing through two points $\left(x_{1}, y_{1}\right)$ and $\left(x_{2}, y_{2}\right)$ is given by

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Substituting the points $(-2,5)$ and $(-1,4)$, we get,

$\begin{aligned}m &=\frac{4-5}{-1+2} \\&=\frac{-1}{1} \\&=-1\end{aligned}$

Thus, the slope is -1.

Thus, the rate of change of the linear relationship is -1.