Question

use a model the table of ordered pairs shows the coordinates of the two points on the graph of a function. write an equation that describes the function.

x	y
-2	2
4	-1

Explanation:

Step1: Find the slope (m)

The formula for slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1, y_1)=(-2, 2)\) and \((x_2, y_2)=(4, -1)\). Then \(m=\frac{-1 - 2}{4 - (-2)}=\frac{-3}{6}=-\frac{1}{2}\).

Step2: Use point - slope form to find the equation

The point - slope form of a line is \(y - y_1=m(x - x_1)\). Using the point \((-2, 2)\) and \(m =-\frac{1}{2}\), we have \(y - 2=-\frac{1}{2}(x - (-2))\). Simplify this: \(y - 2=-\frac{1}{2}(x + 2)\). Distribute the \(-\frac{1}{2}\): \(y - 2=-\frac{1}{2}x-1\). Add 2 to both sides: \(y=-\frac{1}{2}x + 1\).

Answer:

\(y =-\frac{1}{2}x + 1\)