Question

The points (2,-2) and (-4, 13) lie on the graph of a linear equation. What isthe linear equation? *

Answer 1

Answer:

$y=-\frac{5}{2}x+3$

Explanation:

Given the two points on the graph to be (2, -2) and (-4, 13), we can use the point-slope form of the equation of a line below to write the required linear equation;

$y-y_1=m(x-x_1)$

where m = slope of the line

x1 and y1 = coordinates of one of the points

Let's go ahead and determine the slope of the line;

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{13-(-2)}{-4-2}=\frac{13+2}{-6}=-\frac{15}{6}=-\frac{5}{2}$

Let's go ahead and substitute the value of the slope into our point-slope equation using x1 = 2 and y1 = -2;

$\begin{gathered} y-(-2)=-\frac{5}{2}(x-2) \\ y+2=-\frac{5}{2}x+5 \\ y=-\frac{5}{2}x+5-2 \\ y=-\frac{5}{2}x+3 \end{gathered}$