Question

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

Answer 1

Hint: 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!