# What is the slope of the line given by the equation y = -7x - 2?

Mar 30, 2015

All linear functions have an equation of $y = m x + c$

Slope is the change in $y$-axis over $x$-axis. "How the graph behaves for $1$ unit of change in the $x$-axis"

To calculate the slope, we need $2$ different points from the line.

Lets say $A \left(a , b\right)$ and $B \left(k , l\right)$

Slope $= \frac{l - b}{k - a}$

Since $l$ and $b$ are $y$:

Slope = $\frac{\left(m \cdot k + c\right) - \left(m \cdot a + c\right)}{k - a}$

$= \frac{m k + c - m a - c}{k - a}$

$= \frac{m \left(k - a\right)}{k - a} = m$

$m$ being the slope of gradient
$c$ being the y-intercept. Because the line intercepts $y$-axis when $x = 0$

In this case, the Slope($m$) is -7

The equation is given in the standard slope intercept for. The coefficient of x, indicates the slope of the line.