Are the equations in slope-intercept form? What information can the slope-intercept form of an equation give us?
(3,- 3)
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.
Writing in Slope-Intercept Form
Let's rewrite each of the equations in the system in slope-intercept form, highlighting the values of m and b.
Given Equation
Slope-Intercept Form
Slope m
y-intercept b
3y+4x=3
y= -4/3x+ 1
-4/3
(0, 1)
x+3y=- 6
y= -1/3x+( - 2)
-1/3
(0, - 2)
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 straight edge.
We can see that the lines intersect at exactly one point.
