Are the equations in slope-intercept form? What information can the slope-intercept form of an equation give us?
Solution: (1,-1) Explanation: See solution.
Practice makes perfect
In this system of equations, both equations are in slope-intercept form. Therefore, we can determine the number of solutions to the system by graphing the given equations. This will be the point at which the lines intersect.
Identifying Slopes and y-intercepts
The equations in the system are already written in slope-intercept form. Let's identify the slope m and y-intercept b of each line.
Slope-Intercept Form
Slope m
y-intercept b
y=x-2 ⇕ y= 1x+( - 2)
1
(0, - 2)
y= - 2x+ 1
- 2
(0, 1)
Graphing the System
To graph these equations, we will start by plotting their y-intercepts. Then, we will use the slope to determine another point that satisfies each equation, and connect the points with a line.
We can see that the lines intersect at exactly one point.
