Question

Given the line 2 x - 3 y - 5 = 0, find the slope of a line that is perpendicular to this line.

Answer 1

-3/2

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The given line is 2x - 3y - 5 = 0.

To find the slope of a line that is perpendicular to this line, we need to find the slope of the given line and then take its negative reciprocal.

The slope-intercept form of a line is:

• y = mx + b, where m represents the slope

Rearranging the given equation in this form, we get:

• 3y = 2x - 5

And dividing by 3, we get:

• y = (2/3)x - 5/3

So, the slope of the given line is 2/3.

To find the slope of a line perpendicular to this line, we take the negative reciprocal of 2/3, which is -3/2.

Therefore, the slope of a line perpendicular to the given line is -3/2.