Question

Find the equation of the line given the following conditions.

Answer 1

Considering the definition of perpendicular line, you obtain:

1) the equation of perpendicular line is y= -5x + 7.

2) the equation of perpendicular line is y= 7x + 54.

Linear equation

A linear equation o line can be expressed in the form y = mx + b

where

• x and y are coordinates of a point.
• m is the slope.
• b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.

Perpendicular line

Perpendicular lines are lines that intersect at right angles or 90° angles. If you multiply the slopes of two perpendicular lines, you get –1.

Equation of perpendicular line of y=1/5x +6

If you multiply the slopes of two perpendicular lines, you get –1. In this case, the line has a slope of  1/5. So:

1/5× slope perpendicular line= -1

slope perpendicular line= (-1)÷ (1/5)

slope perpendicular line= -5

So, the perpendicular line has a form of: y= -5x + b

The line passes through the point (2,-3). Replacing in the expression for perpendicular line:

-3= -5× (2) + b

-3= -10 + b

-3 +10 = b

7= b

Finally, the equation of perpendicular line is y= -5x + 7.

Equation of perpendicular line of x +7y -12= 0

In this case, the line is x +7y -12= 0. Expressed in the form y = mx + b, you get:

7y= -x +12

y= (-x + 12)÷ 7

y= -1/7x +12/7

If you multiply the slopes of two perpendicular lines, you get –1. In this case, the line has a slope of  -1/7. So:

-1/7× slope perpendicular line= -1

slope perpendicular line= (-1)÷ (-1/7)

slope perpendicular line= 7

So, the perpendicular line has a form of: y= 7x + b

The line passes through the point (5,-9). Replacing in the expression for perpendicular line:

-9= 7× (-9) + b

-9= -63 + b

-9 + 63 = b

54= b

Finally, the equation of perpendicular line is y= 7x + 54.

Summary

In summary, you obtain:

1) the equation of perpendicular line is y= -5x + 7.

2) the equation of perpendicular line is y= 7x + 54.

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