Algebra Examples

Find Any Equation Perpendicular to the Line y=2x
y=2x
Step 1
Choose a point that the perpendicular line will pass through.
(0,0)
Step 2
Use the slope-intercept form to find the slope.
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Step 2.1
The slope-intercept form is y=mx+b, where m is the slope and b is the y-intercept.
y=mx+b
Step 2.2
Using the slope-intercept form, the slope is 2.
m=2
m=2
Step 3
The equation of a perpendicular line must have a slope that is the negative reciprocal of the original slope.
mperpendicular=-12
Step 4
Find the equation of the perpendicular line using the point-slope formula.
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Step 4.1
Use the slope -12 and a given point (0,0) to substitute for x1 and y1 in the point-slope form y-y1=m(x-x1), which is derived from the slope equation m=y2-y1x2-x1.
y-(0)=-12(x-(0))
Step 4.2
Simplify the equation and keep it in point-slope form.
y+0=-12(x+0)
y+0=-12(x+0)
Step 5
Write in y=mx+b form.
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Step 5.1
Solve for y.
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Step 5.1.1
Add y and 0.
y=-12(x+0)
Step 5.1.2
Simplify -12(x+0).
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Step 5.1.2.1
Add x and 0.
y=-12x
Step 5.1.2.2
Combine x and 12.
y=-x2
y=-x2
y=-x2
Step 5.2
Reorder terms.
y=-(12x)
Step 5.3
Remove parentheses.
y=-12x
y=-12x
Step 6
 [x2  12  π  xdx ]