Question

Find the slope of a line perpendicular to the line whose equation is 2x + 2y = 24.

Option 1: -1
Option 2: 1
Option 3: -2
Option 4: 2

Answer 1

To find the slope of a line perpendicular to the given line, first express the given line in slope-intercept form to identify its slope. The slope of a line perpendicular to another is the negative reciprocal of the first line's slope. Therefore, the slope of a line perpendicular to the given line is 1.

Step-by-step explanation:

The question asks to find the slope of a line perpendicular to the given line 2x + 2y = 24. First, we need to find the slope (m) of the given line. We can rewrite the equation in slope-intercept form, y = mx + b, by isolating y:

2y = -2x + 24 ⇒ y = -x + 12

So the slope of the given line is -1. The slopes of two perpendicular lines are negative reciprocals of each other. Therefore, the slope of a line perpendicular to one with a slope of -1 would be the negative reciprocal of -1, which is 1.

The slope of a line perpendicular to the given line is 1, which corresponds to Option 2.