Question

How do you find the x and y intercept of \[y = - 6x - 6\]?

Answer 1

Hint: 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.