Question

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

Answer 1

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
$\begin{aligned} & \Rightarrow \dfrac{0}{4}=\dfrac{4}{4}x \\\ & \Rightarrow 0=x \\\ & \therefore x=0 \\\ \end{aligned}$
$\therefore \text{ we get x-intercept as }A(0,0)$
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

& \Rightarrow y=4(0) \\\ & \therefore y=0 \\\ \end{aligned}$$ $$\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.