# Precalculus 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
Add to both sides of the equation.
Step 4.2.1.2
Step 4.2.2
Subtract from 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
Move the negative in front of the fraction.
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