y=2x-6
You said there was a supplied table, but since you didn't
tell use what it was, we'll have to make one up. It'll
end up the same graph whether you use the supplied values
or the ones I make up below:
Make this chart
x | y
--|--
|
--|--
|
--|--
|
--|--
|
Fill in some arbitrary small numbers for x, or y, say
these below (0 is usually a good number to pick for
either letter since it tells you where the line crosses
the axes:
x | y
--|--
0|
--|--
| 0
--|--
5|
--|--
| 6
Now we fill in the missing values by substituting the
values we chose arbitrarily:
We start with the 0 under x. We substitute (0) for x in the
equation:
y = 2x - 6
y = 2(0) - 6
y = 0 - 6
y = -6
So we fill in the -6 in the y-column beside the 0 in the
x-column, like this:
x | y
--|--
0|-6
--|--
| 0
--|--
5|
--|--
| 6
Next, we go to the 0 under y. We substitute (0) for y in the
equation:
y = 2x - 6
(0) = 2x - 6
0 = 2x - 6
Add -2x to both sides:
-2x = -6
Divide both sides by -2
x = 3
So we fill in the 3 in the x-column beside the 0 in the
y-column, like this:
x | y
--|--
0|-6
--|--
3| 0
--|--
5|
--|--
| 6
Next, we go to the 5 under x. We substitute (5) for x in the
equation:
y = 2x - 6
y = 2(5) - 6
y = 10 - 6
y = 4
So we fill in the 4 in the y-column beside the 5 in the
x-column, like this:
x | y
--|--
0|-6
--|--
3| 0
--|--
5| 4
--|--
| 6
Next, we go to the 6 under y. We substitute (6) for y in the
equation:
y = 2x - 6
(6) = 2x - 6
6 = 2x - 6
Add -2x to both sides:
-2x + 6 = -6
Add -6 to both sides
-2x = -12
Divide both sides by -2
x = 6
So we fill in the 6 in the x-column beside the 6 in the
y-column, like this:
x | y
--|--
0|-6
--|--
3| 0
--|--
5| 4
--|--
6| 6
Those represent the points (x,y) which are
(0,-6), (3,0), (5,4), and (6,6).
We plot those four points like this:
Then we get a ruler and draw this line. Notice how the pointa are
all in a line. Isn't it interesting that they all just happen to
be in a line, even though we just made up those values at random?
It's just like magic!
Edwin
