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Is the equation in slope-intercept form? What information can the slope-intercept form of an equation give you?
(- 8,- 11)
By graphing the given equations, we can solve the system. If a solution exists, it 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.
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+13 | y=3x+ 13 | 3 | (0, 13) |
y= x-3 | y=1x+( -3) | 1 | (0, -3) |
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.
The point of intersection at (-8,-11) is the solution to the system.