Question

What is the slope of a line perpendicular to 3x + 2y = 7?
-2/3
-3/2
3/2
2/3

Answer 1

m = 2/3

Explanation:

Rewrite in slope-intercept form.

y = -3/2x + 7/2

Using the slope-intercept form, the slope is −3/2.

m = -3/2

The equation of a perpendicular line to y=−3/2x + 7/2 must have a slope that is the negative reciprocal of the original slope.

Answer 2

`(2)/(3)`

Explanation:

• First rewrite the original equation in the form y = mx + c ,

where m = gradient:

`3x + 2y = 7`

⇒
`2y = -3x + 7`

⇒
`y = (-3)/(2)x + (7)/(2)`

• From this equation, we can see that the gradient, m =
`(-3)/(2)` .

The gradient of a line perpendicular to another line with gradient m, =
`(-1)/(m)`.

∴ gradient of perpendicular = -1 ÷
`(-3)/(2)`

=
`(2)/(3)`