Question

How do you find the x and y intercept of $- 2x + 3y = 6$?

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, $- 2x + 3y = 6$.
To find the ‘x’ intercept put $y = 0$ in the above equation,
$\Rightarrow - 2x + 3(0) = 6$
$\Rightarrow - 2x = 6$
Divide by $- 2$ on both sides of the equation,
$\Rightarrow x = \dfrac{6}{{ - 2}}$
$\Rightarrow x = - 3$.
Thus ‘x’ intercept is $- 3$.
To find the ‘y’ intercept put $x = 0$ in the above equation,
$\Rightarrow - 2(0) + 3y = 6$
$\Rightarrow 3y = 6$
Divide by 3 on both sides of the equation,
$\Rightarrow y = \dfrac{6}{3}$
$\Rightarrow y = 2$.
Thus ‘y’ intercept is 2.

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