# How do you find the x and y intercept of 3y = 2x + 24?

Jul 28, 2016

$x$ intercept = -12, #y intercept = +8

#### Explanation:

The $x$ intercept of a straight line refers to the (signed) distance from the origin of the point where the line intersects the $x$ axis.

Now, all points on the given line must satisfy the equation

$3 y = 2 x + 24$

On the other hand, any point on the $x$ axis must satisfy $y = 0$. Thus, to obtain the $x$ intercept of a straight line we must substitute $y = 0$ in its equation.

This gives

$2 x + 24 = 0$

and thus $x = - 12$.

Similarly, substituting $x = 0$ gives the $y$ intercept as +8.

Alternatively, we could have expressed the equation of the straight line in the form $\frac{x}{a} + \frac{y}{b} = 1$ and directly read off the values of $a$ and $b$ as the $x$ and $y$ intercepts, respectively.

In this case, rearranging and dividing both sides by 24 gives

$3 y - 2 x = 24 \implies \frac{3 y - 2 x}{24} = 1 \implies \frac{y}{8} - \frac{x}{12} = 1$

or

$\frac{x}{- 12} + \frac{y}{8} = 1$