# How do you find the slope of the line 3x-2y=-8?

Apr 4, 2015

Answer: $\frac{3}{2}$

Solution

Arrange this in the form:

$y = m x + c$

where $m$ is the gradient of the line and $c$ is the y intercept

It goes...
$3 x - 2 y = - 8$

$\implies 2 y = 3 x + 8$

$\implies y = \frac{3}{2} x + 4$

Hence $m = \frac{3}{2}$

ALTERNATIVELY you would differentiate the equation implicitly:

You have $3 x - 2 y = - 8$. Differentiate each term you get,

$3 - 2 \frac{\mathrm{dy}}{\mathrm{dx}} = 0$

$\implies \frac{\mathrm{dy}}{\mathrm{dx}} = \frac{3}{2}$

$\frac{\mathrm{dy}}{\mathrm{dx}}$ is the gradient of the line