Question

How do you find the x and y intercept of $2x - 6y = 18$?

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, $2x - 6y = 18$.
To find the ‘x’ intercept put $y = 0$ in the above equation,
$\Rightarrow 2x - 6(0) = 18$
$\Rightarrow 2x = 18$
Divide by 2 on both sides of the equation,
$\Rightarrow x = \dfrac{{18}}{2}$
$\Rightarrow x = 9$.
Thus ‘x’ intercept is 9.
To find the ‘y’ intercept put $x = 0$ in the above equation,
$\Rightarrow 2(0) - 6y = 18$
$\Rightarrow - 6y = 18$
Divide by ‘-6’ on both sides of the equation,
$\Rightarrow y = - \dfrac{{18}}{6}$
$\Rightarrow y = - 3$.
Thus ‘y’ intercept is -3.
If we draw the graph for the above equation. We will have a line or curve that crosses the x-axis at 9 and y-axis at -3.

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 $2x - 6y = 18$
Now we need 1 on the right hand side of the equation, so divide the whole equation by 18. We have,
$\Rightarrow \dfrac{{2x - 6y}}{{18}} = \dfrac{{18}}{{18}}$
Splitting the terms we have,
$\Rightarrow \dfrac{{2x}}{{18}} - \dfrac{{6y}}{{18}} = \dfrac{{18}}{{18}}$
$\Rightarrow \dfrac{x}{9} - \dfrac{y}{3} = 1$
That is we have,
$\Rightarrow \dfrac{x}{9} + \dfrac{y}{{ - 3}} = 1$. On comparing with standard intercept form we have ‘x’ intercept is 9 and y intercept is -3. In both the cases we have the same answer.