Question

Which of the following points on the XY - graph is the x- intercept of the equation $y = 2x - 8$?
A. $\left( {0,4} \right)$
B. $\left( {0,\dfrac{1}{4}} \right)$
C. $\left( {4,0} \right)$
D. $\left( { - 4,0} \right)$
E. $\left( { - \dfrac{1}{4},0} \right)$

Answer 1

Hint: We can take an arbitrary point on x axis with coordinates $\left( {a,0} \right)$ as the x- intercept of the equation. Then we can substitute the point in the equation of the given line. Now we can solve the equation to get the coordinates of the x intercept.

Complete step-by-step answer:
We have the line $y = 2x - 8$.
We know that the x intercept of a curve is the point at which the curve meets the x axis. We also know that any point on the x axis is of the form $\left( {a,0} \right)$.
Let $\left( {a,0} \right)$ be the x intercept of the given line. As this point lies on the line, it satisfies the equation of the line.
On substituting the point on the line, we get
 $ \Rightarrow 0 = 2a - 8$
On rearranging, we get
 $ \Rightarrow 2a = 8$
On dividing by 2 on both sides, we get
 $ \Rightarrow a = \dfrac{8}{2}$
Hence, we have
 $ \Rightarrow a = 4$
On substituting this value in the coordinate of x intercept we get, $\left( {4,0} \right)$
Therefore, the x- intercept of the equation $y = 2x - 8$ is $\left( {4,0} \right)$
So, the correct answer is option C.

Note: Alternate method to solve this problem is given by,
We have the equation of the line as $y = 2x - 8$. We can rearrange it as,
 $2x - 8 - y = 0$
We know that the x intercept of a curve is the point at which the curve meets the x axis. We also know that any point on the x axis is of the form $\left( {a,0} \right)$.
So, we can eliminate the options A and B.
As the required point lies on the line, it satisfies the equation of the line.
So, consider option C, $\left( {4,0} \right)$.
On substituting it in the equation $2x - 8 - y = 0$, we get
 $ \Rightarrow 2 \times 4 - 8 - 0 = 8 - 8 = 0$
Therefore, $\left( {4,0} \right)$ is a point on the x axis as well as the given line.
Therefore, the x- intercept of the equation $y = 2x - 8$ is $\left( {4,0} \right)$
So, the correct answer is option C.