Question

How do I find the slope of the line $3x-2y=0$ ?

Answer 1

Hint: Slope of a line is defined as the angle made by the line with respect to -axis in a counter-clockwise sense. It can also be represented by using $\tan \theta $ . We can find the slope of the line in two ways. One way is to differentiate it. And the other way is to convert it into the slope intercept form of line and then compare the given line equation to the general intercept form.

Complete step by step answer:
Let’s find the slope of the equation of the given line using differentiation.
Let’s differentiate the line equation with respect to $x$ .Upon differentiation we get the following :
$\Rightarrow $ $3-2\dfrac{dy}{dx}=0$ .
We know that when we differentiate a constant ,it is going to be 0
 $\Rightarrow $ $\dfrac{dk}{dx}=0$ where k is a constant.
We know that $\dfrac{dy}{dx}$ also represents the slope of the line.
 $\Rightarrow \dfrac{dy}{dx}=\dfrac{3}{2}$ .
$\therefore $ Hence ,the slope of the given is $\dfrac{3}{2}$
Just to get an idea of finding the slope using slope- intercept form ,the general equation of the slope- intercept form is $y=mx+c$ , where $m$ represents the slope of the line .Convert the given line equation to this general form and then compare the both to get the slope of the line.

Note:
You can find the slope of the given line equation using the slope intercept as well. But differentiating the given line is a quicker method to complete the process. While doing it using slope intercept form , we have to be careful with comparing the given line equation with the general slope intercept line equation. . We will have to differentiate it with respect to $x$ only to find the slope of a line.