Question

How do you find the x and y intercept of \[2x - 6y = 18\]?

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, \[2x - 6y = 18\].
To find the ‘x’ intercept put \[y = 0\] in the above equation,
\[\Rightarrow 2x - 6(0) = 18\]
\[\Rightarrow 2x = 18\]
Divide by 2 on both sides of the equation,
\[\Rightarrow x = \dfrac{{18}}{2}\]
\[ \Rightarrow x = 9\].
Thus ‘x’ intercept is 9.
To find the ‘y’ intercept put \[x = 0\] in the above equation,
\[\Rightarrow 2(0) - 6y = 18\]
\[\Rightarrow - 6y = 18\]
Divide by ‘-6’ on both sides of the equation,
\[\Rightarrow y = - \dfrac{{18}}{6}\]
\[ \Rightarrow y = - 3\].
Thus ‘y’ intercept is -3.
If we draw the graph for the above equation. We will have a line or curve that crosses the x-axis at 9 and y-axis at -3.

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 \[2x - 6y = 18\]
Now we need 1 on the right hand side of the equation, so divide the whole equation by 18. We have,
\[\Rightarrow \dfrac{{2x - 6y}}{{18}} = \dfrac{{18}}{{18}}\]
Splitting the terms we have,
\[\Rightarrow \dfrac{{2x}}{{18}} - \dfrac{{6y}}{{18}} = \dfrac{{18}}{{18}}\]
\[\Rightarrow \dfrac{x}{9} - \dfrac{y}{3} = 1\]
That is we have,
\[ \Rightarrow \dfrac{x}{9} + \dfrac{y}{{ - 3}} = 1\]. On comparing with standard intercept form we have ‘x’ intercept is 9 and y intercept is -3. In both the cases we have the same answer.