Are the equations in slope-intercept form? What information can the slope-intercept form of an equation give us?
Graph:
Solution: (- 1,- 2)
Practice makes perfect
By graphing the given equations, we can determine the number of solutions to the system. To do this, we will need the equations written in slope-intercept form to help us identify the slope m and y-intercept b. We will start by transforming the equations a little bit.
Write in Slope-Intercept Form
Let's rewrite each of the equations in the system in slope-intercept form, highlighting the m and b values.
Given Equation
Slope-Intercept Form
Slope m
y-intercept b
y=- 3x-5
y= - 3x+( - 5)
- 3
(0, - 5)
y=9x+7
y= 9x+( 7)
9
(0, 7)
Graphing the System
To graph our equations, we will start by plotting their y-intercepts. Then, we will use the slopes to determine another points that satisfies each equation, and connect the points with a line.
The solutions of the system of equations are the points at which the lines intersect. Here, we can see that they intersect at exactly one point.
