# How do you find the slope and intercept of f(x) = 10x-7?

Jul 6, 2016

Slope: $10$
$f \left(x\right)$-intercept: $\left(- 7\right)$
$\textcolor{w h i t e}{\text{XXX}} x$-intercept: $\frac{7}{10}$ (this may/may not) have been required)

#### Explanation:

The general slope-intercept form for a linear equation is
$\textcolor{w h i t e}{\text{XXX}} f \left(x\right) = \textcolor{g r e e n}{m} x + \textcolor{b l u e}{b}$
with slope $\textcolor{g r e e n}{m}$ and $f \left(x\right)$-intercept $\textcolor{b l u e}{b}$

The given equation
$\textcolor{w h i t e}{\text{XXX}} f \left(x\right) = \textcolor{g r e e n}{10} x \textcolor{b l u e}{- 7}$
is in this form with slope $\textcolor{g r e e n}{10}$ and $f \left(x\right)$-intercept color(blue)(""(-7))

If the $x$-intercept is required:
the $x$-intercept is the value of $x$ when $f \left(x\right) = 0$
$\textcolor{w h i t e}{\text{XXX}} 0 = 10 x - 7$
$\textcolor{w h i t e}{\text{XXX}} \rightarrow 10 x = 7$
$\textcolor{w h i t e}{\text{XXX}} \rightarrow x = \frac{7}{10}$

Jul 6, 2016

slope $= 10$ and the y-intercept = $- 7$
The x-intercept is $\frac{7}{10}$

#### Explanation:

Remember that $f \left(x\right)$ is the same as $y$.

$y = 10 x - 7$

This equation is therefore already in the form $y = m x + c$

The slope is 10 (the numerical coefficient of x) and the y-intercept is -7 (c)

To find the x-intercept, make y = 0 and solve for x

$10 x = 7$
$x = \frac{7}{10}$