You will need two points for each equation to draw their graphs.
(2,4)
Practice makes perfect
By graphing the given equations, we can determine the solution to the system. This will be the point at which the lines intersect. To do this, we will need the equations to be in slope-intercept form to help us identify the slope m and y-intercept b.
Write in Slope-Intercept Form
While the given system of equations is already in slope-intercept form, let's rewrite them a little to highlight the m and b values.
Given Equation
Slope-Intercept Form
Slope m
y-intercept b
y=2x
y=2x+ 0
2
(0, 0)
y=-2x+8
y=-2x+ 8
-1
(0, 8)
Graphing the System
To graph these equations, we first plot their y-intercepts. Then, we use the slopes to determine second points that satisfy each equation. We connect these points to give the graphs of the functions.
We can see that the lines intersect at exactly one point.
It appears that the lines intersect at ( 2, 4), so this is the solution to the system.
Checking Our Solution
To check our answer, we will substitute the solution into the given equations. If the substitutions result in true statements, then we know that we have found the correct answer.
