Question

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

Answer 1

`y=-(5)/(2)x+3`

Step-by-step 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=(y_2-y_1)/(x_2-x_1)=(13-(-2))/(-4-2)=(13+2)/(-6)=-(15)/(6)=-(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)=-(5)/(2)(x-2) \\ y+2=-(5)/(2)x+5 \\ y=-(5)/(2)x+5-2 \\ y=-(5)/(2)x+3 \end{gathered}`