Precalculus Examples

Find the Average Rate of Change y-2/7x=5
Step 1
Write as a function.
Step 2
Solve for .
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Step 2.1
Simplify each term.
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Step 2.1.1
Combine and .
Step 2.1.2
Move to the left of .
Step 2.2
Add to both sides of the equation.
Step 3
Consider the difference quotient formula.
Step 4
Find the components of the definition.
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Step 4.1
Evaluate the function at .
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Step 4.1.1
Replace the variable with in the expression.
Step 4.1.2
Simplify the result.
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Step 4.1.2.1
To write as a fraction with a common denominator, multiply by .
Step 4.1.2.2
Simplify terms.
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Step 4.1.2.2.1
Combine and .
Step 4.1.2.2.2
Combine the numerators over the common denominator.
Step 4.1.2.3
Simplify the numerator.
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Step 4.1.2.3.1
Multiply by .
Step 4.1.2.3.2
Apply the distributive property.
Step 4.1.2.4
The final answer is .
Step 4.2
Find the components of the definition.
Step 5
Plug in the components.
Step 6
Simplify.
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Step 6.1
Simplify the numerator.
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Step 6.1.1
Apply the distributive property.
Step 6.1.2
Multiply by .
Step 6.1.3
To write as a fraction with a common denominator, multiply by .
Step 6.1.4
Combine and .
Step 6.1.5
Combine the numerators over the common denominator.
Step 6.1.6
Combine the numerators over the common denominator.
Step 6.1.7
Rewrite in a factored form.
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Step 6.1.7.1
Multiply by .
Step 6.1.7.2
Subtract from .
Step 6.1.7.3
Add and .
Step 6.1.7.4
Subtract from .
Step 6.1.7.5
Add and .
Step 6.2
Multiply the numerator by the reciprocal of the denominator.
Step 6.3
Cancel the common factor of .
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Step 6.3.1
Factor out of .
Step 6.3.2
Cancel the common factor.
Step 6.3.3
Rewrite the expression.
Step 7