Question

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

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Answer 1

The slope of a line that is perpendicular to the given line is
`-(3)/(2)`

Explanation:

The equation of the line in Slope-Intercept form is:

`y=mx+b`

Where "m" is the slope of the line and "b" is the y-intercept.

Solve for "y" from the equation of the line
`2x - 3y - 5 = 0`:

`2x - 3y - 5 = 0\\\\-3y=-2x+5\\\\y=(-2)/(-3)x+(5)/(-3)\\\\y=(2)/(3)x-(5)/(3)`

You can observe that the slope of this line is:

`m=(2)/(3)`

By definition, the slopes of perpendicular lines are negative reciprocal, then, the slope of a line that is perpendicular to the give line, is

`m=-(3)/(2)`