Question

How do you write an equation of a line with Slope = –5, passing through (–4, –2)?

Answer 1

There are a couple of standard forms of equation of a line:

(1) Point slope form: `y-y_0 = m(x - x_0)`, where `m` is the slope and `(x_0, y_0)` is a point on the line.

So we can write the equation of our line as:

`y - (-2) = -5(x - (-4))`

that is:

`y+2 = -5(x+4)`

(2) Slope intercept form: `y = mx + c`, where `m` is the slope and `c` is the intercept - i.e. the `y` coordinate of the intersection of the line with the `y` axis.

Subtracting `mx` from both sides of this line equation, we find that `c = y - mx`.

In our case, substituting our example point `(-4, -2)` and slope `m=-5`, we find:

`c = -2 - (-5)(-4) = -2-20 = -22`

So we can write the equation of our line as:

`y = (-5)x+(-22)`

that is:

`y = -5x-22`