Question

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

Answer 1

All linear functions have an equation of `y=mx+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(a,b)` and `B(k,l)`

Slope `=(l-b)/(k-a)`

Since `l` and `b` are `y`:

Slope = `((m*k +c) - (m*a+c)) / (k-a)`

`=(mk+c-ma-c)/(k-a)`

`=(m(k-a))/(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.