Are the equations in slope-intercept form? What information can the slope-intercept form of an equation give us?
Graph:
Solution: Infinitely many solutions.
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 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=- 2x-5
y= - 2x+( - 5)
- 2
(0, - 5)
6x+3y=- 15
y= - 2x+( - 5)
- 2
(0, - 5)
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. We can see from our graph that the lines are the same. So, every point on the line is a solution to the system, which means that there are infinitely many solutions.
Showing Our Work
Showing Our Work
Here, we can take a look at how to transform the equations into slope-intercept form. This process requires the following calculations.
