Question

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

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, $4y - x = 3$.
To find the ‘x’ intercept put $y = 0$ in the above equation,
$4(0) - x = 3$
$- x = 3$
Multiply by -1 on both sides of the equation,
$\Rightarrow x = - 3$.
Thus ‘x’ intercept is $- 3$.
To find the ‘y’ intercept put $x = 0$ in the above equation,
$4y - (0) = 3$
$4y = 3$
Divide by 4 on both sides of the equation,
$y = \dfrac{3}{4}$
$\Rightarrow y = 0.75$.
Thus ‘y’ intercept is 0.75.
If we draw the graph for the above equation. We will have a line or curve that crosses the x-axis at $- 3$ and y-axis at 0.75.

Note: We can solve this using the standard intercept form. That is the equation of line which cuts off intercepts ‘a’ and ‘b’ respectively from ‘x’ and ‘y’ axis is $\dfrac{x}{a} + \dfrac{y}{b} = 1$. We convert the given equation into this form and compare it will have a desired result.
Given $4y - x = 3$
Now we need 1 on the right hand side of the equation, so divide the whole equation by 3. We have,
$\dfrac{{4y - x}}{3} = \dfrac{3}{3}$
Splitting the terms we have,
$\dfrac{{4y}}{3} - \dfrac{x}{3} = \dfrac{3}{3}$
$- \dfrac{x}{3} + \dfrac{{4y}}{3} = \dfrac{3}{3}$
That is we have,
$\Rightarrow \dfrac{x}{{ - 3}} + \dfrac{y}{{0.75}} = 1$. On comparing with standard intercept form we have ‘x’ intercept is -3 and y intercept is 0.75. In both the cases we have the same answer.