Question

How do you find the x and y-intercept of $4x + 8y = 12$?

Answer 1

Hint: This is a linear equation of the first order. In this question, a linear equation is given. We will convert this equation into the form of a straight-line equation. Then put the value of x is equal to 0 to find the y-intercept. Then convert this equation in terms of x. And put the value of y is equal to 0 to find the x-intercept.

Complete step-by-step answer:
In this question, the linear equation is
$ \Rightarrow 4x + 8y = 12$
Let us take out 4 as a common factor from both sides.
Therefore,
$ \Rightarrow x + 2y = 3$
Let us subtract x on both sides.
$ \Rightarrow x - x + 2y = 3 - x$
Therefore,
$ \Rightarrow 2y = 3 - x$
Now, let us divide both sides by 2.
$ \Rightarrow y = \dfrac{{3 - x}}{2}$
Let us split the denominator.
$ \Rightarrow y = \dfrac{{ - x}}{2} + \dfrac{3}{2}$ ...(1)
Now, to find the value of y-intercept we will put the value of x is 0 in equation (1).
$ \Rightarrow y = \dfrac{{ - 0}}{2} + \dfrac{3}{2}$
So, the y-intercept is,
$ \Rightarrow y = \dfrac{3}{2}$
Now, to find the value of x-intercept we will put the value of y as 0 in equation (1).
$ \Rightarrow 0 = \dfrac{{ - x}}{2} + \dfrac{3}{2}$
Now, find the least common multiple of the denominator on the right-hand side.
 $ \Rightarrow 0 = \dfrac{{ - x + 3}}{2}$
Let us multiply both sides by 2.
$ \Rightarrow 0 \times 2 = \dfrac{{ - x + 3}}{2} \times 2$
That is equal to
$ \Rightarrow 0 = - x + 3$
Now, let us add x on both sides.
$ \Rightarrow 0 + x = - x + x + 3$
So,
$ \Rightarrow x = 3$

Hence, the value of x-intercept is 3 and the value of y-intercept is$\dfrac{3}{2}$.

Note:
The x-intercept is where a line crosses the x-axis, and the y-intercept is the point where the line crosses the y-axis. In the question, we can say that the value of x-intercept is 3. So, the point on the x-axis is $\left( {3,0} \right)$. And the value of y-intercept is $\dfrac{3}{2}$. So, the point on the y-axis is $\left( {0,\dfrac{3}{2}} \right)$.