# What is the slope intercept form of the line with a slope of -2/5  and y-intercept of  -4/7 ?

Dec 5, 2016

Simple: $y = - \frac{2}{5} x - \frac{4}{7}$.

#### Explanation:

Slope-intercept form $\left(y = m x + b\right)$ is called that because those two pieces of information (the slope $m$ and the $y$-intercept $b$) are seen directly in the formula.

Since we are given the value for slope as $m = - \frac{2}{5}$ and the value for the $y$-intercept as $b = - \frac{4}{7}$, we simply plug these two values into the raw formula and simplify to arrive at

$y = \text{ "m" "x+" } b$

$y = \left(- \frac{2}{5}\right) x + \left(- \frac{4}{7}\right)$

$y = - \frac{2}{5} x - \frac{4}{7.}$

The slope tells you how fast $y$ changes relative to $x$ (in this case, $- \frac{2}{5}$ times as fast), and the $y$-intercept tells you the value of $y$ when $x = 0.$ If you plug $x = 0$ into the equation, you get

$y = - \frac{2}{5} \left(0\right) - \frac{4}{7}$

$\textcolor{w h i t e}{y} = - \frac{4}{7.}$