Question

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

Answer 1

Answer:

$\frac{2}{3}$

Step-by-step explanation:

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

where m = gradient:

$3x + 2y = 7$

⇒ $2y = -3x + 7$

⇒ $y = \frac{-3}{2}x + \frac{7}{2}$

• From this equation, we can see that the gradient, m = $\frac{-3}{2}$ .

The gradient of a line perpendicular to another line with gradient m,  = $\frac{-1}{m}$.

∴ gradient of perpendicular = -1  ÷   $\frac{-3}{2}$

                                              = $\frac{2}{3}$    

Answer 2

Answer:

m = 2/3

Step-by-step 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.