How do you graph y = $ \dfrac{1}{4}x-3 $ by plotting points?

Hint: Here in this question, we have to solve the equation given which is a linear equation in two variables. We will use the general form of the equation of slope and intercept to solve this problem. The general form of this equation is:
y = mx + c
where m is the slope and c is the constant.
 After that, we will put the values for ‘x’ in order to find the value for ‘y’ for a corresponding value of ‘x’. Then plot all the values in a graph to obtain the line.

Complete step by step answer:
Now, let’s solve the question.
We already know that the slope-intercept form is a general form of a straight line and is expressed as y = mx + c where ‘m’ is a slope and c is a constant and intercepts are m and c.
So, for plotting a straight line, first, we have to convert the given equation into a slope-intercept form. Let’s study how!
First, write the equation from the question.
 $ \Rightarrow $ y = $ \dfrac{1}{4}x-3......(i) $
As we can observe that the above equation is already in general form of straight line i.e. y = mx + c, here m = $ \dfrac{1}{4} $ and c = -3.
Now, we have to find the intercepts for x and y.
Let’s find y-intercept first. Substitute x = 0 in equation(i) we get:
 $ \Rightarrow $ y = $ \dfrac{1}{4}(0)-3 $
Now we get the value of ‘y’ as:
 $ \Rightarrow $ y = -3
 $ \therefore $ y-intercept form is: $ \left( 0,-3 \right) $
Similarly, we will find x-intercept now. Put y = 0 in equation(i) we get:
 $ \Rightarrow $ (0) = $ \dfrac{1}{4}x-3 $
Now, take 3 on the left side, the sign will get change:
 $ \Rightarrow $ 3 = $ \dfrac{1}{4}x $
As $ \dfrac{1}{4} $ is in product with ‘x’, now it will be reciprocated and taken to the left side:
 $ \Rightarrow 3\times \dfrac{4}{1}=x $
Now the value of x will be:
 $ \Rightarrow $ x = 12
 $ \therefore $ x-intercept will be: (12, 0)
Let’s plot the graph of the equation with the help of the intercepts.


The graph above is of y-intercept: (0, -3).


The graph above is of x-intercept: (12, 0).

Note:
We plotted the points by slope and intercept form so that it becomes easy to solve for a particular variable. It is the easiest approach to finding the coordinates. All you need to know the general form of the equation of a straight line. If you are not obtaining a straight line after plotting the points, it means you are going wrong somewhere in the calculation.