Question

How do you find the x and y intercepts of 6y = 3x + 6?

Answer 1

We will first put in x = 0 in the given equation 6y = 3x + 6 to find the y – intercept and then we will put in y = 0 in the given equation 6y = 3x + 6 to find the x – intercept.

Complete step by step solution:
We are given that we need to find the x and y intercepts of 6y = 3x + 6.
We need to put in x = 0, when we are trying to find the y – intercept and we will put in y = 0, when we find the x – intercept.
Let us put in x = 0 in the given equation 6y = 3x + 6.
Therefore, we have: 6y = 0 + 6
Simplifying it, we will then obtain the following equation with us:-
$\Rightarrow$ 6y = 6
Dividing both the sides of the above equation by 6, we will then obtain the following equation with us:-
$\Rightarrow$ y = 1
Hence, the y – intercept of the given line 6y = 3x + 6 is 1.
Let us put in y = 0 in the given equation 6y = 3x + 6.
Therefore, we have: 0 = 3x + 6
Taking 6 from addition in the left hand side to subtraction in the right hand side and re – arranging the terms in above equation, we will then obtain the following equation with us:-
$\Rightarrow$ 3x = - 6
Dividing both the sides of the above equation by 3, we will then obtain the following equation with us:-
$\Rightarrow$ x = - 2

Hence, the x – intercept of the given line 6y = 3x + 6 is – 2.

Note:
The students must note that the x – intercepts and y – intercepts are basically the points where the given equation of line cuts the y – axis and x – axis at.
Finding the intercepts gives us two points on the equation of line directly and then we can just join those points to find the equation of the line and thus, we have the graph.
The students must also know that if we convert the given equation in slope – intercept form, then it is easy to find the intercepts directly.