Question

How do you find the x and y intercept of $$3x+4y=12$$ ?

Answer 1

Hint: We know that x-intercept is a point on the graph where ‘y’ is zero. Also we know that y-intercept is a point on the graph where ‘x’ is zero. In other words the value of ‘x’ at ‘y’ is equal to zero is called x-intercept. The value of ‘y’ at ‘x’ is equal to zero is called t-intercept. Using this definition we can solve the given problem.

Complete step-by-step answer:
Given,
 $$3x+4y=12$$ .
To find the x-intercept we substitute $$y=0$$ in the given equation we have,
 $$3x+4(0)=12$$
 $$3x=12$$
Dividing by 3 on both side of the equation we have
 $$x={\displaystyle \frac{12}{3}}$$
 $$x=4$$
That is x-intercept is 4.
To find the y-intercept we substitute $$x=0$$ in the given equation we have,
 $$3(0)+4y=12$$
 $$4y=12$$
Divide the whole equation by 4 we have,
 $$y={\displaystyle \frac{12}{4}}$$
 $$y=3$$ .
That is y-intercept is 3.
Thus, we have the x-intercept is 4. The y-intercept is 3.
So, the correct answer is “ x-intercept is 4 and The y-intercept is 3”.

Note: We can also solve this by converting the given equation into the equation of straight line intercept form. That is $${\displaystyle \frac{x}{a}}+{\displaystyle \frac{y}{b}}=1$$ . Where ‘a’ is a x-intercept and ‘b’ is called y-intercept.
Now given,
 $$3x+4y=12$$
We need 1 on the right hand side of the equation. So we divide the equation by 12 on both sides.
 $${\displaystyle \frac{3x+4y}{12}}={\displaystyle \frac{12}{12}}$$
Separating the terms in the left hand side of the equation. We have,
 $${\displaystyle \frac{3x}{12}}+{\displaystyle \frac{4y}{12}}={\displaystyle \frac{12}{12}}$$
Now cancelling we have,
 $${\displaystyle \frac{x}{4}}+{\displaystyle \frac{y}{3}}=1$$ .
Now comparing with the standard intercept equation we have,
The x-intercept is 4. The y-intercept is 3. In both the methods we have the same answer. We can choose any one method to solve this.