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Algebra Examples
Through ; perpendicular to the line
Step 1
Step 1.1
Move all terms not containing to the right side of the equation.
Step 1.1.1
Subtract from both sides of the equation.
Step 1.1.2
Subtract from both sides of the equation.
Step 1.2
Divide each term in by and simplify.
Step 1.2.1
Divide each term in by .
Step 1.2.2
Simplify the left side.
Step 1.2.2.1
Cancel the common factor of .
Step 1.2.2.1.1
Cancel the common factor.
Step 1.2.2.1.2
Divide by .
Step 1.2.3
Simplify the right side.
Step 1.2.3.1
Simplify each term.
Step 1.2.3.1.1
Move the negative in front of the fraction.
Step 1.2.3.1.2
Move the negative in front of the fraction.
Step 2
Step 2.1
Rewrite in slope-intercept form.
Step 2.1.1
The slope-intercept form is , where is the slope and is the y-intercept.
Step 2.1.2
Write in form.
Step 2.1.2.1
Reorder terms.
Step 2.1.2.2
Remove parentheses.
Step 2.2
Using the slope-intercept form, the slope is .
Step 3
The equation of a perpendicular line must have a slope that is the negative reciprocal of the original slope.
Step 4
Step 4.1
Cancel the common factor of and .
Step 4.1.1
Rewrite as .
Step 4.1.2
Move the negative in front of the fraction.
Step 4.2
Multiply the numerator by the reciprocal of the denominator.
Step 4.3
Multiply by .
Step 4.4
Multiply .
Step 4.4.1
Multiply by .
Step 4.4.2
Multiply by .
Step 5
Step 5.1
Use the slope and a given point to substitute for and in the point-slope form , which is derived from the slope equation .
Step 5.2
Simplify the equation and keep it in point-slope form.
Step 6
Step 6.1
Solve for .
Step 6.1.1
Simplify .
Step 6.1.1.1
Rewrite.
Step 6.1.1.2
Simplify by adding zeros.
Step 6.1.1.3
Apply the distributive property.
Step 6.1.1.4
Combine and .
Step 6.1.1.5
Multiply by .
Step 6.1.2
Move all terms not containing to the right side of the equation.
Step 6.1.2.1
Subtract from both sides of the equation.
Step 6.1.2.2
To write as a fraction with a common denominator, multiply by .
Step 6.1.2.3
Combine and .
Step 6.1.2.4
Combine the numerators over the common denominator.
Step 6.1.2.5
Simplify the numerator.
Step 6.1.2.5.1
Multiply by .
Step 6.1.2.5.2
Subtract from .
Step 6.2
Reorder terms.
Step 7