Question

How do you graph 2x – 3y + 15 = 0?

Answer 1

Hint: We will first put x = 0 and then find the value of y. Now, we will put x = 3 and find the value of y. Now, we will plot these two points and then join them to form the line.

Complete step by step answer:
We are given that we are required to graph 2x – 3y + 15 = 0.
Taking 15 from addition in the left hand side to subtraction in the right hand side, we will then obtain the following equation with us:-
$ \Rightarrow $ 2x – 3y = - 15 ………………..(1)
Now, if we put in x = 0, we will then obtain the following expression:-
$ \Rightarrow $ 2 (0) – 3y = - 15
Simplifying the calculations in the left hand side of the above equation, we will then obtain the following equation with us:-
$ \Rightarrow $ - 3y = - 15
Dividing both the sides of the above equation by - 3, we will then obtain the following expression:-
$ \Rightarrow $ y = 5
Thus, we have a point (0, 5) which lies on the line.
Now, if we put in x = 3, we will then obtain the following expression:-
$ \Rightarrow $ 2 (3) – 3y = - 15
Simplifying the calculations in the left hand side of the above equation, we will then obtain the following equation with us:-
$ \Rightarrow $6 - 3y = - 15
Taking 6 from addition in the left hand side to subtraction in the right hand side, we will then obtain the following equation with us:-
$ \Rightarrow $ - 3y = - 15 – 6
Simplifying the calculations on the right hand side of the above equation, we will then obtain the following equation:-
$ \Rightarrow $ - 3y = - 21
Dividing both the sides of the above equation by - 3, we will then obtain the following expression:-
$ \Rightarrow $ y = 7
Thus, we have a point (3, 7) which lies on the line.
Plotting these points on the graph and joining them to form a line, we will then obtain the following equation with us:-

Note: The students most note that there is an alternate way to do the same question.
We will first convert the given equation in slope – intercept form as follows:-
The given equation is 2x – 3y + 15 = 0
Taking 2x and 15 from addition in the left hand side to subtraction in the right hand side, we will then obtain the following equation:-
\[ \Rightarrow \] – 3y = - 2x – 15
Dividing the whole equation by – 3, we will then obtain the following equation:-
\[ \Rightarrow y = \dfrac{2}{3}x + 5\]
Thus, we see that the y – intercept is + 5 and the slope is 2/3. Therefore, we will get the following graph with us:-