# What are the excluded values for y=7/(5x-10)?

Mar 28, 2017

$x = 2$

#### Explanation:

The only excluded values in this problem would be asymptotes, which are values of $x$ that make the denominator equal to $0$. Since we cannot divide by $0$, this creates a point that is "undefined" or excluded.

In the case of this problem, we are looking for a value of $x$ that makes $5 \cdot x - 10$ equal to zero. So let's set that up:
$5 x - 10 = 0$
$\textcolor{w h i t e}{5 x} + 10 \textcolor{w h i t e}{0} + 10$
$5 x = 10$
$/ 5 \textcolor{w h i t e}{x}$$/ 5$
$x = \frac{10}{5}$ or $2$

So, when $x = 2$, the the denominator becomes equal to zero. So that's the value we must exclude to avoid an asymptote. We can confirm this using a graph
graph{y=7/(5x-10)}

See, the graph is getting closer and closer to $x = 2$, but it can never reach that point.