Precalculus Examples

Find the Slope for Each Equation
,
Use the slope-intercept form to find the slope.
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The slope-intercept form is , where is the slope and is the y-intercept.
Using the slope-intercept form, the slope is .
Use the slope-intercept form to find the slope.
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The slope-intercept form is , where is the slope and is the y-intercept.
Using the slope-intercept form, the slope is .
Set up the system of equations to find any points of intersection.
Solve the system of equations to find the point of intersection.
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Eliminate the equal sides of each equation and combine.
Move all terms containing to the left side of the equation.
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Since contains the variable to solve for, move it to the left side of the equation by subtracting from both sides.
Subtract from to get .
Since does not contain the variable to solve for, move it to the right side of the equation by adding to both sides.
Divide each term by and simplify.
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Divide each term in by .
Simplify the left side of the equation by cancelling the common factors.
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Reduce the expression by cancelling the common factors.
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Move the negative one from the denominator of .
Simplify the expression.
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Multiply by to get .
Rewrite as .
Divide by to get .
Replace all occurrences of with the solution found by solving the last equation for . In this case, the value substituted is .
Multiply by to get .
Solve for in the second equation.
The solution to the system of equations can be represented as a point.
Since the slopes are different, the lines will have exactly one intersection point.
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