Question

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

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, $y = - 6x - 6$.
To find the ‘x’ intercept put $y = 0$ in the above equation,
$\Rightarrow 0 = - 6x - 6$
$\Rightarrow 6x = - 6$
Divide by 6 on both sides of the equation,
$\Rightarrow x = \dfrac{{ - 6}}{6}$
$\Rightarrow x = - 1$.
Thus ‘x’ intercept is $- 1$.
To find the ‘y’ intercept put $x = 0$ in the above equation,
$\Rightarrow y = - 6(0) - 6$
$\Rightarrow y = - 6$
Thus ‘y’ intercept is $- 6$.

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