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

1 Answer
May 24, 2015

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#