Question

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

Answer 1

Hint: To find the $y$ -intercept, let’s substitute $x = 0$ into the equation and solve for $y$ . Similarly, to find the $x$ -intercept, let’s substitute $y = 0$ into the equation and solve for $x$ . The points obtained will be the $y$ -intercept and $x$ -intercept respectively.

Complete step-by-step solution:
Here, we’ve to determine the intercept of the graph described by the following linear equation:
$3x - 4y = 12$
To find the $y$ -intercept, let’s substitute $x = 0$ into the equation and solve for $y$ .
$\Rightarrow$$3\left( 0 \right) - 4y = 12$
Simplifying $3\left( 0 \right) - 4y = 12$ , we get
$\Rightarrow$$ - 4y = 12$
Divide both sides of the equation by $ - 4$ , we get
$\Rightarrow$$y = - 3$
So, the $y$ -intercept is $\left( {0, - 3} \right)$ .
To find the $x$ -intercept, let’s substitute $y = 0$ into the equation and solve for $x$ .
$\Rightarrow$$3x - 4\left( 0 \right) = 12$
Simplifying $3x - 4\left( 0 \right) = 12$ , we get
$\Rightarrow$$3x = 12$
Divide both sides of the equation by $3$ , we get
$\Rightarrow$$x = 4$
So, the $x$-intercept is $\left( {4,0} \right)$ .

Therefore, for $3x - 4y = 12$ , $x$ -intercept is $\left( {4,0} \right)$ and $y$ -intercept is $\left( {0, - 3} \right)$.

Note: We know that the $x$ -intercept is the point where a line crosses the $x$ -axis, and the $y$ -intercept is the point where a line crosses the $y$ -axis.
So, we can determine the intercepts by looking at the graph of a given function.
Graph of $3x - 4y = 12$:

The line crosses the axes at two points. The point on the $x$ -axis is $\left( {4,0} \right)$ . We call this the $x$-intercept.
The point on the $y$ -axis is $\left( {0, - 3} \right)$ . We call this the $y$ -intercept.
Therefore, for $3x - 4y = 12$, $x$ -intercept is $\left( {4,0} \right)$ and $y$ -intercept is $\left( {0, - 3} \right)$ .
We can also determine the intercepts of a given equation by comparing it to standard form for the intercept.
The standard form for the intercept is:
$\dfrac{x}{a} + \dfrac{y}{b} = 1$ , where $a$ is $x$ -intercept and $b$ is $y$ -intercept.
Given equation is $3x - 4y = 12$ .
So, first we have to make the denominator $1$ .
Thus, dividing both sides of the equation by $12$ , we get
$\dfrac{x}{4} - \dfrac{y}{3} = 1$
It can be written as $\dfrac{x}{4} + \dfrac{y}{{\left( { - 3} \right)}} = 1$
Compare it with $\dfrac{x}{a} + \dfrac{y}{b} = 1$ , we get
$a = 4$ and $b = - 3$
Therefore, for $3x - 4y = 12$ , $x$ -intercept is $\left( {4,0} \right)$ and $y$ -intercept is $\left( {0, - 3} \right)$ .