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
 \[x = \dfrac{{12}}{3}\]
 \[x = 4\]
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,
 \[y = \dfrac{{12}}{4}\]
 \[y = 3\] .
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 \[\dfrac{x}{a} + \dfrac{y}{b} = 1\] . 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.
 \[\dfrac{{3x + 4y}}{{12}} = \dfrac{{12}}{{12}}\]
Separating the terms in the left hand side of the equation. We have,
 \[\dfrac{{3x}}{{12}} + \dfrac{{4y}}{{12}} = \dfrac{{12}}{{12}}\]
Now cancelling we have,
 \[\dfrac{x}{4} + \dfrac{y}{3} = 1\] .
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.