Question

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

Answer 1

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.