# Algebra Examples

Find the Slope for Each Equation
,
Step 1
Use the slope-intercept form to find the slope.
Step 1.1
The slope-intercept form is , where is the slope and is the y-intercept.
Step 1.2
Using the slope-intercept form, the slope is .
Step 2
Use the slope-intercept form to find the slope.
Step 2.1
The slope-intercept form is , where is the slope and is the y-intercept.
Step 2.2
Using the slope-intercept form, the slope is .
Step 3
Set up the system of equations to find any points of intersection.
Step 4
Solve the system of equations to find the point of intersection.
Step 4.1
Eliminate the equal sides of each equation and combine.
Step 4.2
Solve for .
Step 4.2.1
Move all terms containing to the left side of the equation.
Step 4.2.1.1
Subtract from both sides of the equation.
Step 4.2.1.2
Subtract from .
Step 4.2.2
Add to both sides of the equation.
Step 4.2.3
Divide each term in by and simplify.
Step 4.2.3.1
Divide each term in by .
Step 4.2.3.2
Simplify the left side.
Step 4.2.3.2.1
Cancel the common factor of .
Step 4.2.3.2.1.1
Cancel the common factor.
Step 4.2.3.2.1.2
Divide by .
Step 4.2.3.3
Simplify the right side.
Step 4.2.3.3.1
Divide by .
Step 4.3
Evaluate when .
Step 4.3.1
Substitute for .
Step 4.3.2
Multiply by .
Step 4.4
The solution to the system is the complete set of ordered pairs that are valid solutions.
Step 5
Since the slopes are different, the lines will have exactly one intersection point.
Step 6