Question

What is the slope of a line perpendicular to the line whose equation is 3x + y = -9.

Answer 1

Considering the definition of perpendicular line, the slope of a line perpendicular to the line whose equation is 3x+y= -9 is  $\frac{1}{3}$.

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.

Two nonvertical lines are perpendicular if the slope of one is the negative reciprocal of the slope of the other. In other words, if you multiply the slopes of two perpendicular lines, you get –1.

Equation of perpendicular line in this case

In this case, the line is 3x+y=-9. Expressed in the form y = mx + b, you get: y= -9 - 3x or, what is the same, y= -3x -9

If you multiply the slopes of two perpendicular lines, you get –1. In this case, the line has a slope of  -3. So:

(-3)× slope perpendicular line= -1

slope perpendicular line= (-1)÷ (-3)

slope perpendicular line=  $\frac{1}{3}$

Finally, the slope of a line perpendicular to the line whose equation is 3x+y= -9 is  $\frac{1}{3}$.

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