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Finite Math Examples
,
Step 1
Step 1.1
The slope-intercept form is , where is the slope and is the y-intercept.
Step 1.2
Subtract from both sides of the equation.
Step 1.3
Divide each term in by and simplify.
Step 1.3.1
Divide each term in by .
Step 1.3.2
Simplify the left side.
Step 1.3.2.1
Cancel the common factor of .
Step 1.3.2.1.1
Cancel the common factor.
Step 1.3.2.1.2
Divide by .
Step 1.3.3
Simplify the right side.
Step 1.3.3.1
Simplify each term.
Step 1.3.3.1.1
Divide by .
Step 1.3.3.1.2
Cancel the common factor of and .
Step 1.3.3.1.2.1
Factor out of .
Step 1.3.3.1.2.2
Cancel the common factors.
Step 1.3.3.1.2.2.1
Factor out of .
Step 1.3.3.1.2.2.2
Cancel the common factor.
Step 1.3.3.1.2.2.3
Rewrite the expression.
Step 1.3.3.1.2.2.4
Divide by .
Step 1.4
Reorder and .
Step 2
Using the slope-intercept form, the slope is .
Step 3
Step 3.1
The slope-intercept form is , where is the slope and is the y-intercept.
Step 3.2
Subtract from both sides of the equation.
Step 3.3
Divide each term in by and simplify.
Step 3.3.1
Divide each term in by .
Step 3.3.2
Simplify the left side.
Step 3.3.2.1
Cancel the common factor of .
Step 3.3.2.1.1
Cancel the common factor.
Step 3.3.2.1.2
Divide by .
Step 3.3.3
Simplify the right side.
Step 3.3.3.1
Simplify each term.
Step 3.3.3.1.1
Divide by .
Step 3.3.3.1.2
Cancel the common factor of and .
Step 3.3.3.1.2.1
Factor out of .
Step 3.3.3.1.2.2
Cancel the common factors.
Step 3.3.3.1.2.2.1
Factor out of .
Step 3.3.3.1.2.2.2
Cancel the common factor.
Step 3.3.3.1.2.2.3
Rewrite the expression.
Step 3.3.3.1.3
Move the negative in front of the fraction.
Step 3.4
Write in form.
Step 3.4.1
Reorder and .
Step 3.4.2
Reorder terms.
Step 3.4.3
Remove parentheses.
Step 4
Using the slope-intercept form, the slope is .
Step 5
Set up the system of equations to find any points of intersection.
Step 6
Step 6.1
Solve for in .
Step 6.1.1
Subtract from both sides of the equation.
Step 6.1.2
Divide each term in by and simplify.
Step 6.1.2.1
Divide each term in by .
Step 6.1.2.2
Simplify the left side.
Step 6.1.2.2.1
Cancel the common factor of .
Step 6.1.2.2.1.1
Cancel the common factor.
Step 6.1.2.2.1.2
Divide by .
Step 6.1.2.3
Simplify the right side.
Step 6.1.2.3.1
Simplify each term.
Step 6.1.2.3.1.1
Divide by .
Step 6.1.2.3.1.2
Cancel the common factor of and .
Step 6.1.2.3.1.2.1
Factor out of .
Step 6.1.2.3.1.2.2
Cancel the common factors.
Step 6.1.2.3.1.2.2.1
Factor out of .
Step 6.1.2.3.1.2.2.2
Cancel the common factor.
Step 6.1.2.3.1.2.2.3
Rewrite the expression.
Step 6.1.2.3.1.3
Move the negative in front of the fraction.
Step 6.2
Replace all occurrences of with in each equation.
Step 6.2.1
Replace all occurrences of in with .
Step 6.2.2
Simplify the left side.
Step 6.2.2.1
Simplify .
Step 6.2.2.1.1
Simplify each term.
Step 6.2.2.1.1.1
Apply the distributive property.
Step 6.2.2.1.1.2
Multiply by .
Step 6.2.2.1.1.3
Cancel the common factor of .
Step 6.2.2.1.1.3.1
Move the leading negative in into the numerator.
Step 6.2.2.1.1.3.2
Factor out of .
Step 6.2.2.1.1.3.3
Cancel the common factor.
Step 6.2.2.1.1.3.4
Rewrite the expression.
Step 6.2.2.1.1.4
Multiply by .
Step 6.2.2.1.2
Add and .
Step 6.3
Solve for in .
Step 6.3.1
Move all terms not containing to the right side of the equation.
Step 6.3.1.1
Subtract from both sides of the equation.
Step 6.3.1.2
Subtract from .
Step 6.3.2
Divide each term in by and simplify.
Step 6.3.2.1
Divide each term in by .
Step 6.3.2.2
Simplify the left side.
Step 6.3.2.2.1
Cancel the common factor of .
Step 6.3.2.2.1.1
Cancel the common factor.
Step 6.3.2.2.1.2
Divide by .
Step 6.3.2.3
Simplify the right side.
Step 6.3.2.3.1
Divide by .
Step 6.4
Replace all occurrences of with in each equation.
Step 6.4.1
Replace all occurrences of in with .
Step 6.4.2
Simplify the right side.
Step 6.4.2.1
Simplify .
Step 6.4.2.1.1
Simplify each term.
Step 6.4.2.1.1.1
Divide by .
Step 6.4.2.1.1.2
Multiply by .
Step 6.4.2.1.2
Subtract from .
Step 6.5
The solution to the system is the complete set of ordered pairs that are valid solutions.
Step 7
Since the slopes are different, the lines will have exactly one intersection point.
Step 8