Question

How do you find the $x$ and $y$ intercepts for $3x - 4y = 12$?

Answer 1

In this problem, we have given an equation and here we are asked to find the $x$ and $y$ intercept of the given equation and geometrically to solve this problem we need to substitute some value for $x$ to find the $x$ intercept and also substitute one value for $y$ to find the $y$ intercept.

Complete step-by-step answer:
The given equation is $3x - 4y = 12$.
There are two axes in the graph. In that, the x-intercept is the value of $x$ when the value of $y$ is equal to zero.
This implies that when we substitute the value of $y$ is equal to zero the given equation becomes,
$\Rightarrow 3x - 4\left( 0 \right) = 12$
Multiplication of any number with zero is again zero. So the above equation becomes,
$\Rightarrow 3x - 0 = 12$
Simplify the terms,
$\Rightarrow 3x = 12$
Divide both sides by 3,
$\Rightarrow x = 4$
So, the x-intercept is 4.
Now, the y-intercept is the value of $y$ when the value of $x$ is equal to zero.
This implies that when we substitute the value of $x$ is equal to zero the given equation becomes,
$\Rightarrow 3\left( 0 \right) - 4y = 12$
Simplify the terms,
$\Rightarrow - 4y = 12$
Divide both sides by -4,
$\Rightarrow y = - 3$
So, the y-intercept is -3.

Hence, the x-intercept is 4 and the y-intercept is -3.

Note:
The intercepts of a graph are points at which the graph crosses the axes. The x-intercept is the point at which the graph crosses the x-axis. At this point, the y-coordinate is zero. The y-intercept is the point at which the graph crosses the y-axis. At this point, the x-coordinate is zero.
It is to be noted that we can also write the intercept points for both the x and y-axis. The intercept point for the x-axis would be (4,0) since the x-intercept is 4 and similarly the intercept point for the y-axis would be (0,-3) since the y-intercept is -3.