Algebra 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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Subtract from both sides of the equation.
Subtract from .
Divide each term by and simplify.
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Divide each term in by .
Reduce the expression by cancelling the common factors.
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Cancel the common factor.
Divide by .
Solve for in the first equation.
Replace all occurrences of with the solution found by solving the last equation for . In this case, the value substituted is .
Simplify the right side.
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To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Combine.
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
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Multiply by .
Add and .
Solve for in the second equation.
List the solutions to the system of equations.
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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