Finite Math Examples

Find the Perpendicular Line (-1,3) , 6x+3y=1
,
Step 1
Solve .
Tap for more steps...
Step 1.1
Subtract from both sides of the equation.
Step 1.2
Divide each term in by and simplify.
Tap for more steps...
Step 1.2.1
Divide each term in by .
Step 1.2.2
Simplify the left side.
Tap for more steps...
Step 1.2.2.1
Cancel the common factor of .
Tap for more steps...
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.
Tap for more steps...
Step 1.2.3.1
Cancel the common factor of and .
Tap for more steps...
Step 1.2.3.1.1
Factor out of .
Step 1.2.3.1.2
Cancel the common factors.
Tap for more steps...
Step 1.2.3.1.2.1
Factor out of .
Step 1.2.3.1.2.2
Cancel the common factor.
Step 1.2.3.1.2.3
Rewrite the expression.
Step 1.2.3.1.2.4
Divide by .
Step 2
Find the slope when .
Tap for more steps...
Step 2.1
Rewrite in slope-intercept form.
Tap for more steps...
Step 2.1.1
The slope-intercept form is , where is the slope and is the y-intercept.
Step 2.1.2
Reorder and .
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
Simplify to find the slope of the perpendicular line.
Tap for more steps...
Step 4.1
Move the negative in front of the fraction.
Step 4.2
Multiply .
Tap for more steps...
Step 4.2.1
Multiply by .
Step 4.2.2
Multiply by .
Step 5
Find the equation of the perpendicular line using the point-slope formula.
Tap for more steps...
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
Write in form.
Tap for more steps...
Step 6.1
Solve for .
Tap for more steps...
Step 6.1.1
Simplify .
Tap for more steps...
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.
Tap for more steps...
Step 6.1.2.1
Add to 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.
Tap for more steps...
Step 6.1.2.5.1
Multiply by .
Step 6.1.2.5.2
Add and .
Step 6.2
Reorder terms.
Step 7