Question

What are the intercepts for \[y = 6x + 8\]?

Answer 1

Hint: We need to find x and y intercept. 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, \[y = 6x + 8\].
To find the ‘x’ intercept put \[y = 0\] in the above equation,
\[0 = 6x + 8\]
\[6x = - 8\]
Divide by 6 on both sides of the equation,
\[x = \dfrac{{ - 8}}{6}\]
\[ \Rightarrow x = \dfrac{{ - 4}}{3}\]
or
\[ \Rightarrow x = - 1.333\].
Thus ‘x’ intercept is \[ - 1.333\].
To find the ‘y’ intercept put \[x = 0\] in the above equation,
\[y = 6(0) + 8\]
\[ \Rightarrow y = 8\].
Thus ‘y’ intercept is 8.

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 to the desired result.
Given \[y = 6x + 8\] or \[6x - y = - 8\]
Now we need 1 on the right hand side of the equation, so divide the whole equation by -8. We have,
\[\dfrac{{6x - y}}{{ - 8}} = \dfrac{{ - 8}}{{ - 8}}\]
Splitting the terms we have,
\[\dfrac{{6x}}{{ - 8}} + \dfrac{{ - y}}{{ - 8}} = 1\]
That is we have,
\[ \Rightarrow \dfrac{x}{{ - 1.33}} + \dfrac{y}{8} = 1\]
On comparing with standard intercept form we have ‘x’ intercept is \[ - 1.333\] and y intercept is 8. In both cases we have the same answer.