# How do you find the slope of y=7/5x-2?

Oct 15, 2015

Slope: $\frac{7}{5}$

#### Explanation:

The slope-intercept form of a linear equation is
$\textcolor{w h i t e}{\text{XXX}} y = \textcolor{red}{m} x + \textcolor{b l u e}{b}$
$\textcolor{w h i t e}{\text{XXXXXX}}$where $\textcolor{red}{m}$ is the slope and $\textcolor{b l u e}{b}$ is the y-intercept.

$y = \frac{7}{5} x - 2 \iff y = \textcolor{red}{\frac{7}{5}} x + \textcolor{b l u e}{\left(- 2\right)}$

$\textcolor{w h i t e}{\text{XXX}}$is in this form

$\rightarrow$ slope $= \textcolor{red}{\frac{7}{5}}$

Alternative (if you don't know or are told not to use the slope-intercept form)

Slope $= m = \frac{\Delta y}{\Delta x}$

Pick two values for which $y = \frac{7}{5} x - 2$ is easy to calculate
(e.g. $x = 0$ and $x = 5$) to get

Slope $= m = \frac{{y}_{x = 5} - {y}_{x = 0}}{5 - 0}$

$\textcolor{w h i t e}{\text{XXXXXXX}} = \frac{5 - \left(- 2\right)}{5} = \frac{7}{5}$