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.
$\Rightarrow y={\displaystyle \frac{3-x}{2}}$
Let us split the denominator.
$\Rightarrow y={\displaystyle \frac{-x}{2}}+{\displaystyle \frac{3}{2}}$ ...(1)
Now, to find the value of y-intercept we will put the value of x is 0 in equation (1).
$\Rightarrow y={\displaystyle \frac{-0}{2}}+{\displaystyle \frac{3}{2}}$
So, the y-intercept is,
$\Rightarrow y={\displaystyle \frac{3}{2}}$
Now, to find the value of x-intercept we will put the value of y as 0 in equation (1).
$\Rightarrow 0={\displaystyle \frac{-x}{2}}+{\displaystyle \frac{3}{2}}$
Now, find the least common multiple of the denominator on the right-hand side.
 $\Rightarrow 0={\displaystyle \frac{-x+3}{2}}$
Let us multiply both sides by 2.
$\Rightarrow 0\times 2={\displaystyle \frac{-x+3}{2}}\times 2$
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${\displaystyle \frac{3}{2}}$.

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 ${\displaystyle \frac{3}{2}}$. So, the point on the y-axis is $\left(0,{\displaystyle \frac{3}{2}}\right)$.