Question

The x and y intercepts of the following line is:
$y - 3x = 0$ :
A.$a = 0,{\text{ }}b = 3$
B.$a = 0,{\text{ }}b = 0$
C.$a = 0,{\text{ }}b = - 3$
D.$a = 0,{\text{ }}b = \dfrac{1}{3}$

Answer 1

Hint: In the given question, we are first required to convert the given equation in the form of $y = mx + b$, where m is the slope of the line and b is the y-intercept. Then compare the obtained equation with this general form to find the y-intercept. For finding the x-intercept, put y=0 in the given equation.

Complete step by step Answer:

Let the x-intercept be a and the y-intercept be b.
Let us begin by considering the given equation, which is;
$y - 3x = 0$
We convert this equation into the standard form, $y = mx + b$, where m is the slope of the line and b is the y-intercept
$y = 3x + 0$ ……(1)

Now, we compare the obtained equation with$y = mx + b$ to find the value of the y-intercept b.
$ \Rightarrow b = 0$

We find the x-intercept by putting y=0 in (1).
$
   \Rightarrow 0 - 3x = 0 \\
   \Rightarrow x = 0 \\
 $

Thus, we get that the value of x-intercept is a=0 and that of y-intercept b also equals 0.

Hence, option (B) is the correct option.


Note: While solving these kinds of questions, involving equations of a line give proper attention to its conversion to some standard form of the equation. As for example in this question, we converted the given equation to the general form is given by, $y = mx + b$. Once we have done this, we directly got our y-intercept just by comparing the two equations. This will actually save your time and calculation errors too.