Question

Find the equation of the line that contains the point
P(−4, −4)
and is perpendicular to the graph of
y = − 4/5x − 1

Answer 1

Considering the definition of perpendicular line,  the equation of of perpendicular line is y= 5/4x -9.

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 in this case

The line is y= -4/5x - 1.

If you multiply the slopes of two perpendicular lines, you get –1. In this case, the line has a slope of -4/5. So:

-4/5× slope perpendicular line= -1

slope perpendicular line= (-1)÷ (-4/5)

slope perpendicular line= 5/4

So, the perpendicular line has a form of: y= 5/4x + b

The line passes through the point (-4, -4). Replacing in the expression for parallel line:

-4= 5/4×(-4) + b

-4= 5 + b

-4 -5 = b

-9 = b

Finally, the equation of of perpendicular line is y= 5/4x -9.

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