Swap sides:
Divide both sides by 8 to solve for y
It is not possible to get whole numbers for y using whole
numbers for x, because the numerator will always be odd,
since it's an even number (4x) plus an odd number (3) and
therefore it can never be divisible by 8.
So we have no choice but to put up with fractions.
We make a t-chart. I arbitrarily choose 5 for x
x | y
5 |
|
|
Now I substitute 5 for x in the equation:
Fraction numbers are easier to plot when expressed as a decimal:
x | y
5 | 2.875
|
|
The point (5,2.875) is between the points (5,2) and (5,3), a little
bit below (5,3) because 2.875 is a tiny bit below (5,3). I'll draw
(5,2) and (5,3) in green and the point (5,2.875) in black:
Now I'll take the green points away. I just put them there to
show you that you just have to guess where points with fraction
coordinates are located, as they are in between the points with whole
number coordinates.
-----
Now I arbitrarily choose another value for x, say -4
x | y
5 | 2.875
-4 |
|
Now I substitute 5 for x in the equation:
Fraction numbers are easier to plot when expressed as a decimal:
x | y
5 | 2.875
-4 |-1.625
|
To plot (-4,-1.625) is between the points (-4,1) and (-4,2), a little
bit closer to (-4,2) because .625 is a little more than halfway between
them, which would be (-4,-1.5). I'll draw (-4,-1) and (-4,-2) in green and the point (-4,-1.625) in black:
Now I'll take the green points away. As before, I just put them
there to show you that you just have to guess where points with fraction
coordinates are located, as they are in between the points with whole
number coordinates.
Now I could draw a line through them. However in case I made a mistake
I should plot a third point as a check. Then if it doesn't line up with the
other two so that I cannot draw a line through all three points, then I'll know
I made an error somewhere. If it lines up so that I can draw a line through
all three points, then I'll know I'm right.
-----
So I arbitrarily choose a third value for x as a check, say 1
x | y
5 | 2.875
-4 |-1.625
1 |
Now I substitute 1 for x in the equation:
Fraction numbers are easier to plot when expressed as a decimal:
x | y
5 | 2.875
-4 |-1.625
1 | .875
The point (1,.875) is between the points (1,0) and (1,1), a little
bit below (1,1) because .875 is a tiny bit below (1,1). I'll draw
(1,0) and (1,1) in green and the point (1,.875) in black:
Now I'll take the green points away. As before, I just put them
there to show you that you just have to guess where points with fraction
coordinates are located, as they are in between the points with whole
number coordinates.
Now let's see if we can draw a line through all three
points. If I can I'll draw it in blue:
Edwin
