Question

How do you find the x intercepts of $2x - 6y = 26$?

Answer 1

Here we need to find x-intercept and y-intercept. We know that x-intercept is a point on the graph where ‘y’ is zero. Also we know that y-intercept is a point on the graph where ‘x’ is zero. In other words the value of ‘x’ at ‘y’ is equal to zero is called x-intercept. The value of ‘y’ at ‘x’ is equal to zero is called t-intercept. Using this definition we can solve the given problem.

Complete step-by-step solution:
Given,
$\Rightarrow 2x - 6y = 26$.
To find the x-intercept we substitute $y = 0$ in the given equation we have,
$\Rightarrow 2x - 6\left( 0 \right) = 26$
$\Rightarrow 2x = 26$
Dividing by 2 on both side of the equation we have
$\Rightarrow x = \dfrac{{26}}{2}$
$\Rightarrow x = 13$
That is x-intercept is 13.
To find the y-intercept we substitute $x = 0$ in the given equation we have,
$\Rightarrow 2\left( 0 \right) - 6y = 26$
$\Rightarrow - 6y = 26$
Dividing by -6 on both side of the equation we have
$\Rightarrow y = - \dfrac{{26}}{6}$
$\Rightarrow y = - \dfrac{{13}}{3}$
or
$\Rightarrow y = - 4.33$
That is y-intercept is -4.33.

Thus, we have the x-intercept is 13. The y-intercept is -4.33.

Note: We can also solve this by converting the given equation into the equation of straight line intercept form. That is $\dfrac{x}{a} + \dfrac{y}{b} = 1$. Where ‘a’ is a x-intercept and ‘b’ is called y-intercept.
Now given,
$2x - 6y = 26$
We need 1 on the right hand side of the equation. So we divide the equation by 26 on both sides.
$\dfrac{{2x - 6y}}{{26}} = \dfrac{{26}}{{26}}$
Separating the terms in the left hand side of the equation. We have,
$\dfrac{{2x}}{{26}} + \dfrac{{ - 6y}}{{26}} = 1$
Now cancelling we have,
$\dfrac{x}{{13}} + \dfrac{y}{{ - 4.33}} = 1$.
Now comparing with the standard intercept equation we have,
The x-intercept is 13. The y-intercept is -4.33. In both the methods we have the same answer. We can choose any one method to solve this.