Question

How would you find the slope of the line $3x - 2y = 4$?

Answer 1

We are given an equation of line in the form $ax - by = c$ and we have to find the slope of the line. For that first we will convert those into the standard form i.e. slope intercept form $y = mx + c$. So first we will keep y-term on one side i.e. $ax - c = by$. Now we will divide the whole equation by the coefficient of y. We get the equation in this form $\dfrac{a}{b}x - \dfrac{c}{b}$. Then we will compare this equation with the slope intercept form of line i.e. $y = mx + c$ and find the value of slope.

Complete step by step answer:
Step1:
We are given an equation of line i.e.$3x - 2y = 4$. So first we will arrange the terms and put y-terms on one side. Terms of $x$ and constant term on one side. Then we will get:
$3x - 4 = 2y$

Step2:
Then we will divide the whole equation by the coefficient of y i.e. 2. On dividing we get:
$\Rightarrow \dfrac{3}{2}x - 2 = y$
On rearrangement we get:
$\Rightarrow y = \dfrac{3}{2}x - 2$
On comparing the equation with standard equation of the line i.e. $y = mx + c$
On comparing we will get:
$\Rightarrow m = \dfrac{3}{2}$

Note: In this type of questions by seeing this form of equation of line. Students get confused and try to find the coordinates of the line. But if the line is given then just convert that equation into the standard form of line. In comparison we will get the value of slope. In case the equation is given in this form only. Then it is the easiest and simple method that we have used in this question is the easiest and simple method to find the slope or y intercept of the equation.