The first step in graphing a line is to graph the y-intercept. Since the line is already written in the slope-intercept formula, this is very easy. The line crosses the y-axis at -1, so you can graph the first point on the line, (0,-1)
From here there are two different ways you can go about graphing the line:
A) You can solve y=-3x-1 twice, substituting a different number for x each time. For example, you can substitute both 1 and -1 for x like so
y = -3x - 1 y = -3x - 1
y = -3(1)-1 y = -3(-1) -1
y = -3 -1 y = 3 -1
y = -4 y = 2
(1, -4) (-1,2)
Plot those two points, or two others of your choice, on a coordinate plane, along with the y-intercept, and connect with a line. Make sure to always use two different points, or a total of three to check your work. If they do not all connect in a straight line, one of them is incorrect and you should check your work.
B) In my opinion, this method is much simpler, but often teachers will prefer the other one.This requires the line be in the slope-intercept form.
The line y = -3x -1 has a slope of -3. -3, written as a fraction, is -[tex] - \frac{3}{1} [/tex] This means that once you have graphed at least one point already (in this case the y-intercept), you can simply move right one and down three to follow the line if that description makes any sense.
As this question is fairly visual, I will try to attach a graph of the line.I'm sorry that it's in a powerpoint, I couldn't find another easy way to make it and attach to here.
