Question

How do you find the slope of the line given by the equation $3x - 4y = 12$?

Answer 1

In this question we have to find the slope of the line given, we can do this by using Slope-intercept form which is given by $y = mx + b$ , where $m$ is the slope of the line and $b$ is the y-intercept of the line, now first convert the given equation into slope intercept form, then by comparing the two equations we will get the required slope.

Complete step by step solution:
Given equation of the line is $3x - 4y = 12$,
Now convert the equation given into slope intercept form which is given by $y = mx + b$ , where $m$ is the slope of the line and $b$ is the y-intercept of the line,
So, given equation is $3x - 4y = 12$,
Now subtract $3x$ from both sides of the equation we get,
$\Rightarrow 3x - 4y - 3x = 12 - 3x$,
Now simplifying we get,
$\Rightarrow - 4y = 12 - 3x$,
Now dividing both sides of the equation with -4 we get,
$\Rightarrow \dfrac{{ - 4y}}{{ - 4}} = \dfrac{{12 - 3x}}{{ - 4}}$,
Now simplifying we get,
$\Rightarrow y = \dfrac{{12}}{{ - 4}} - \dfrac{{3x}}{{ - 4}}$,
Now further simplifying we get,
$\Rightarrow y = - 3 + \dfrac{{3x}}{4}$,
Now rewriting the equation we get,
$\Rightarrow y = \dfrac{{3x}}{4} - 3$, this is in form of slope intercept form,
Now comparing the equation with the slope intercept form which is $y = mx + b$,
On comparing here $m = \dfrac{3}{4}$ and $b = - 3$,
So we know that m is the slope of the line, now $\dfrac{3}{4}$ is the slope of the given line.

$\therefore$ The slope of the line given by the equation $3x - 4y = 12$ is equal to $\dfrac{3}{4}$.

Note:
Remember that if the slope of a line is equal to zero then it is parallel to x-axis and if the slope tends to infinity then it is perpendicular to x-axis. Also, we can remember that if the x-coordinates of the two points through which the line passes are same it must be perpendicular to the x-axis and y-coordinates of the two points through which the line passes are same it must be parallel to the x-axis.