Are the equations in slope-intercept form? What information can the slope-intercept form of an equation give us?
Solution: (2,1) Graph:
Practice makes perfect
By graphing the given equations, we can determine solutions to the system. These will be the points at which the lines intersect. To do this, we will need the equations to be in slope-intercept form to help us identify their slopes m and y-intercepts b.
Write in Slope-Intercept Form
Let's rewrite each of the equations in the system in slope-intercept form, highlighting the slopes m and y-intercepts b.
Given Equation
Slope-Intercept Form
Slope m
y-intercept b
y=x-1
y= 1x+( - 1)
1
(0, - 1)
y=- x+3
y= - 1x+ 3
- 1
(0, 3)
Graphing the System
To graph these equations, we will start by plotting their y-intercepts. Then, we will use the slopes 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.
The point of intersection at (2,1) is the solution to the system.
Checking the Solution
To check our solution we will substitute x= 2 and y= 1 in the system and simplify.
y=x-1 & (I) y=- x+3 & (II)
(I), (II):x= 2, y= 1
1? = 2-1 1? =- 2+3
(I), (II):Add and subtract terms
1=1 1=1
Since both statements are true, we know that our solution is correct.
