Question

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

Answer 1

In this problem, we have been given a linear equation. And we are asked to find the slope of the given line equation. To find the slope of the given linear equation, we need to use slope intercept form. So, we will convert the equation into slope-intercept form. In that slope intercept form, there will be $x$ term and the coefficient of $x$ is the slope.

Formula used: The slope intercept form is $y = mx + c$ , where $m$ is the slope of a given linear equation and $c$ is the $y -$ intercept

Complete step by step answer:
The given line equation is $3x - 2y = 4$
The given linear equation is of the form $ax + by = c$
Now, let’s subtract $3x$ from both sides of the given line equation. We get,
$3x - 2y - 3x = 4 - 3x$ , cancelling $+ 3x$ and $- 3x$ , we get,
$\Rightarrow - 2y = 4 - 3x$
Now divide each term of the above equation by $- 2$
$\dfrac{{ - 2y}}{{ - 2}} = \dfrac{4}{{ - 2}} - \dfrac{{3x}}{{ - 2}}$ . Here, in the left-hand side there is a $- 2$ in both numerator and denominator so they get cancelled by each other and simplifying the first term of right-hand side, we get,
$y = - 2 + \dfrac{{3x}}{2}$ . Rewriting the equation, we get,
$y = \dfrac{{3x}}{2} - 2$ …. (1)
Use the slope-intercept form to find the slope and$y -$ intercept
The slope intercept form is $y = mx + b$ , where $m$ is the slope of a given linear equation and $b$ is the $y -$ intercept.
Now, let us compare equation (1) with the slope intercept formula, we get,
$m = \dfrac{3}{2}$ And $b = - 2$
The slope of the line is the value of $m$ and the $y -$ intercept is the value of $b$ .

Therefore, slope $= \dfrac{3}{2}$ , $y -$ intercept $= - 2$

Note: We can also find the slope of the given linear equation by comparing the given line equation with $ax + by = c$ and then we write the values of $a,b,c$ . In such cases, the formula to be used to calculate slope is $- \dfrac{a}{b}$ . Now substitute the values of $a,b$ in the formula, the value of slope is $\dfrac{{ - 3}}{{ - 2}}$ , cancelling the negative side in the numerator and denominator we get $\dfrac{3}{2}$ .