Question

How do you find the x and y intercept of \[3x - 2y = 15\]?

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, \[3x - 2y = 15\].
To find the ‘x’ intercept put \[y = 0\] in the above equation,
\[3x - 2(0) = 15\]
\[3x = 15\]
Divide by 3 on both sides of the equation,
\[x = \dfrac{{15}}{3}\]
\[ \Rightarrow x = 5\].
Thus ‘x’ intercept is 5.
To find the ‘y’ intercept put \[x = 0\] in the above equation,
\[3(0) - 2y = 15\]
\[ - 2y = 15\]
Divide by \[ - 2\] on both sides of the equation,
\[\Rightarrowy = - \dfrac{{15}}{2}\]
\[ \Rightarrow y = - 7.5\].
Thus ‘y’ intercept is \[ - 7.5\].

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 \[3x - 2y = 15\]
Now we need 1 on the right hand side of the equation, so divide the whole equation by 15. We have,
\[\dfrac{{3x - 2y}}{{15}} = \dfrac{{15}}{{15}}\]
Splitting the terms we have,
\[\Rightarrow \dfrac{{3x}}{{15}} - \dfrac{{2y}}{{15}} = \dfrac{{15}}{{15}}\]
\[\Rightarrow \dfrac{x}{5} - \dfrac{y}{{7.5}} = 1\]
That is we have,
\[ \Rightarrow \dfrac{x}{5} + \dfrac{y}{{ - 7.5}} = 1\]. On comparing with standard intercept form we have ‘x’ intercept is 5 and y intercept is \[ - 7.5\]. In both the cases we have the same answer.