Precalculus Examples

Find the Equation Using Point-Slope Formula
,
Step 1
Find the slope of the line between and using , which is the change of over the change of .
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Step 1.1
Slope is equal to the change in over the change in , or rise over run.
Step 1.2
The change in is equal to the difference in x-coordinates (also called run), and the change in is equal to the difference in y-coordinates (also called rise).
Step 1.3
Substitute in the values of and into the equation to find the slope.
Step 1.4
Simplify.
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Step 1.4.1
Simplify the numerator.
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Step 1.4.1.1
Multiply by .
Step 1.4.1.2
Subtract from .
Step 1.4.2
Simplify the denominator.
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Step 1.4.2.1
Multiply by .
Step 1.4.2.2
Add and .
Step 1.4.3
Move the negative in front of the fraction.
Step 2
Use the slope and a given point to substitute for and in the point-slope form , which is derived from the slope equation .
Step 3
Simplify the equation and keep it in point-slope form.
Step 4
Solve for .
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Step 4.1
Simplify .
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Step 4.1.1
Rewrite.
Step 4.1.2
Simplify by adding zeros.
Step 4.1.3
Apply the distributive property.
Step 4.1.4
Combine and .
Step 4.1.5
Multiply .
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Step 4.1.5.1
Multiply by .
Step 4.1.5.2
Combine and .
Step 4.1.5.3
Multiply by .
Step 4.1.6
Simplify each term.
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Step 4.1.6.1
Move to the left of .
Step 4.1.6.2
Move the negative in front of the fraction.
Step 4.2
Move all terms not containing to the right side of the equation.
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Step 4.2.1
Add to both sides of the equation.
Step 4.2.2
To write as a fraction with a common denominator, multiply by .
Step 4.2.3
Combine and .
Step 4.2.4
Combine the numerators over the common denominator.
Step 4.2.5
Simplify the numerator.
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Step 4.2.5.1
Multiply by .
Step 4.2.5.2
Add and .
Step 5
Reorder terms.
Step 6
Remove parentheses.
Step 7
List the equation in different forms.
Slope-intercept form:
Point-slope form:
Step 8
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