Question

How do you find the x and y intercepts for $y=4x$ ?

Answer 1

Hint: In this question, we need to find the value of x and y-intercepts, for that, we use the Substitution Method. An intercept is a point on the x-axis or y-axis through which the slope of the line passes. This implies that for the y-intercept, the y-coordinate of a point lies on the line or the curve and which passes through the y-axis, similarly for the x-intercept. Thus, for finding the x-intercept, we simply put the value y=0 in the equation and make the necessary calculations to get the value for x. Similarly for the y-intercept, we put x=0 in the equation and step by step solve for y, which is our required answer.

Complete answer:
According to the question, we have to find the value of x-intercept and y-intercept.
So, it is given that the equation is: $y=4x$ ---------- (1)
Thus, by implying the Substitution method in equation (1), that is
For x-intercept:
Let the coordinate be \[A\left( x,y \right)\] .
So to find x-coordinate, let us substitute\[y=0\] in equation (1),
Thus x-intercept \[A\left( x,y \right)\] will become$A(x,0)$ , we get
\[\Rightarrow 0=4x\]
Now, on dividing both the sides by 4, we get
$\begin{align}
  & \Rightarrow \dfrac{0}{4}=\dfrac{4}{4}x \\
 & \Rightarrow 0=x \\
 & \therefore x=0 \\
\end{align}$
\[\therefore \text{ we get x-intercept as }A(0,0)\]
Similarly, for y – intercept:
Let the coordinate as\[B(x,y)\] .
So for y-coordinate, let \[x=0\]in equation (1),
Thus y-intercept \[B(x,y)\] will become$B(0,y)$ , we get
\[\begin{align}
  & \Rightarrow y=4(0) \\
 & \therefore y=0 \\
\end{align}\]
\[\therefore \text{ we get y-intercept as }B(0,0)\]
Graph for the equation $y=4x$ with x-intercept A (0, 0) and y-intercept B (0, 0) is,

Therefore, from the graph, we see that both the x-intercept and the y-intercept have the same value as (0, 0), which implies the equation $y=4x$ passes through the origin.
Thus, we get the value of x-intercept is \[A\left( x,0 \right)=A\left( 0,0 \right)\] and, the value of y-intercept is \[B(0,y)=B(0,0)\] for the equation $y=4x$ .

Note: For such types of questions, you should always keep in mind that for the x-intercept, always substitute y=0 in the equation instead of x=0. Similarly, for y-intercept, put x=0 in the equation and not y=0, which implies that you always substitute the value of the coordinates correctly for finding the intercepts. We can also find the x-intercept and y-intercept using a simpler method, that is by comparing the given equation with $\dfrac{x}{a}+\dfrac{y}{b}=1$ , and then solve for x and y.