Question

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

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, \[ - 2x + 3y = 6\].
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.