Question

How do you find the slope and y-intercept of $3x - 2y = 12$ ?

Answer 1

Given is an equation with two variables x and y. but it is not in standard slope intercept form of a line. We know that standard slope intercept form is $y = mx + c$ where m is the slope. Thus using the rearrangements and transpositions in the equation given we will convert it into standard form. It mainly needs the coefficient of $y$ to be compulsory one. Then in order to find the y intercept we will put x equals to zero.

Complete step-by-step solution:
Given is the equation of the form $3x - 2y = 12$
Now we will shift the terms one by one to make the coefficient of y equals to one.
First we will shift the term with x as coefficient.
$- 2y = 12 - 3x$
Now dividing both sides by 2 we get,
$- y = 6 - \dfrac{3}{2}x$
Rearranging the terms as per standard slope intercept form,
$- y = - \dfrac{3}{2}x + 6$
Multiplying both sides by minus sign we get,
$y = \dfrac{3}{2}x - 6$
This can be called as standard slope intercept form $y = mx + c$ with slope equals to $\dfrac{3}{2}$.
Now in order to find the y intercept we will substitute x as zero.
$y = \dfrac{3}{2} \times 0 - 6$
On multiplying we get,
$y = - 6$
This is the y intercept.

Therefore the slope is $\dfrac{3}{2}$ and y intercept $y = - 6$

Note: Note that writing the given equation in slope intercept form is simply a procedure of steps to be followed such that the coefficient of y should be one. That equation involves slope of the line and intercept. In order to find x- intercept we put y equals to zero and to find y- intercept we put x equals to zero. That’s it!