Question

How do you find the x and y intercept of $4x + 3y = 0$?

Answer 1

x-intercept can be found by substituting the value of ‘y’ is equal to zero in the given equation. Similarly we can find the y-intercept by substituting the value of ‘x’ equal to zero in the given equation. In other words ‘x’ intercept is defined as a line or a curve that crosses the x-axis of a graph and ‘y’ intercept is defined as a line or a curve crosses the y-axis of a graph.

Complete step-by-step solution:
Given, $4x + 3y = 0$.
To find the ‘x’ intercept put $y = 0$ in the above equation,
$\Rightarrow 4x + 3(0) = 0$
$\Rightarrow 4x = 0$
Divide by 4 on both sides of the equation,
$\Rightarrow x = \dfrac{0}{4}$
We know that zero divided by any real number is always zero.
$\Rightarrow x = 0$.
Thus ‘x’ intercept is 0.
To find the ‘y’ intercept put $x = 0$ in the above equation,
$\Rightarrow 4(0) + 3y = 0$
$\Rightarrow 3y = 0$
Divide by 3 on both sides of the equation,
$\Rightarrow y = \dfrac{0}{3}$
$\Rightarrow y = 0$.
Thus ‘y’ intercept is 0.
If we draw the graph for the above equation. We will have a line or curve that crosses the x-axis at 0 and y-axis at 0. That is the line passes through the origin.

Note: We can solve this using the standard intercept form. That is $y = mx + c$. Where ‘m’ is slope and ‘c’ is y-intercept. We have
$4x + 3y = 0$
Rearranging we have,
$3y = - 4x$
Divide the whole equation by 3,
$y = - \dfrac{4}{3}x$
That is
$y = - \dfrac{4}{3}x + 0$.
Compared with the standard form we have slope is $- \dfrac{4}{3}$ and ‘y’ intercept is 0. If we want an ‘x’ intercept, put the value of ‘y’ equal to zero. We will have an ‘x’ intercept equal to zero. In both the cases we have the same answer.