# How do you find the range of y = 3x + 10?

Sep 20, 2015

The range of this function is the whole of $\mathbb{R}$ since for any value of $y$ there is a value of $x$ such that $y = 3 x + 10$

#### Explanation:

We can solve for $x$ in terms of $y$ as follows:

Subtract $10$ from both sides to get:

$y - 10 = 3 x$

Divide both sides by $3$ to get:

$x = \frac{y - 10}{3}$

The right hand side is defined for any $y \in \mathbb{R}$, so we can always find an $x$ that yields a given value of $y$.