# How do you find the intercepts for -3x-4y=18?

Nov 6, 2015

$x = - 6$

$y = - \frac{9}{2}$

#### Explanation:

To find the $x$ and $y$ intercepts for an equation, you need to put the equation in Standard Form ($y = m x + b$).

Thus, we need to solve $- 3 x - 4 y = 18$ for $y$.

First, we can add $3 x$ to both sides. Doing so yields:

=$- 4 y = 18 + 3 x$

or

=$- 4 y = 3 x + 18$

Then, we need to divide both sides by $- 4$ to isolate $y$.

$y = \frac{3 x + 18}{- 4}$

Simplifying slightly gets you:

$y = - \frac{3 x}{4} - \frac{18}{4}$

which equates to

$y = - \frac{3 x}{4} - \frac{9}{2}$

Now that we have the equation in Standard form, we can look for the intercepts. Conceptually, an $x$-intercept will occur when $y = 0$ and a $y$-intercept will occur when $x = 0$.

So, simply plug in those values of $0$ seperately to solve for each intercept.

Solving for the $x$-intercept:

$\left(0\right) = - \frac{3 x}{4} - \frac{9}{2}$

Adding $\frac{3 x}{4}$ to both sides results in:

$\frac{3 x}{4} = - \frac{9}{2}$

Multiplying both sides by $\frac{4}{3}$ gets:

$x = \left(- \frac{9}{2}\right) \left(\frac{4}{3}\right)$

or:

$x = - 6$

Solving for the $y$-intercept:

$y = - \frac{3 \left(0\right)}{4} - \frac{9}{2}$

Canceling out the term with the $0$ being multiplied to it gives:

$y = - \frac{9}{2}$

It is worthy to notice that the y-intercept of the equation, when put in Standard Form, is simply the term without the $x$ in it (or the $b$ term when written as $y = m x + b$).