# How do you find the x and y intercepts for f(x) = -3x-2?

Aug 11, 2016

y-intercept: $- 2$

x-intercept: $- \frac{2}{3}$

#### Explanation:

Note that $f \left(x\right)$ is equivalent to $y$.

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The y-intercept is the value on the Y-axis where the function crosses the Y-axis. Since the Y-axis is the collection of points where $x = 0$, it follows that the y-intercept is the value of the function when $x = 0$.

Evaluating $f \left(x\right) = - 3 x - 2$ when $x = 0$:
$\textcolor{w h i t e}{\text{XXX}} f \left(0\right) = - 3 \left(0\right) - 2 = - 2$
So the y-intercept is at $\left(- 2\right)$

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Similarly, the x-intercept is the value of $x$ when $y = 0$ (or equivalently when $f \left(x\right) = 0$

Evaluating $f \left(x\right) = - 3 x - 2$ when $f \left(x\right) = 0$
$\textcolor{w h i t e}{\text{XXX}} 0 = - 3 x - 2$

$\textcolor{w h i t e}{\text{XXX}} \rightarrow - 3 x = 2$

$\textcolor{w h i t e}{\text{XXX}} \rightarrow x = - \frac{2}{3}$
So the x-intercept is at $\left(- \frac{2}{3}\right)$

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