Q: Graph x + 2y = 4
A: We are going to graph this by making an x-y table of values. A typical (though not necessary) thing to do is solve for y first — this just means “get y by itself”
So, start with the equation:
x + 2y = 4
Subtract x from both sides (to try to get y alone)
2y = 4 – x
Now, it’s standard for to list the x first, so we may write this as:
2y = -x + 4
To get y by itself, divide everything by 2:
y = -x/2 + 4/2
This simplifies to:
y = -1/2 x + 2
So, to make a table of values, pick some numbers for x. It is standard to pick “0, 1, 2” or something similar. So:
x | 0 | 1 | 2 |
y | | | |
Plug in each value for x to find y:
When x = 0, y = -1/2 (0) + 2 = 0 + 2 = 2
When x = 1, y = -1/2 (1) + 2 = -1/2 + 2 = 1.5
When x = 2, y = -1/2 (2) + 2 = -1 + 2 = 1
Then the table is complete:
x | 0 | 1 | 2 |
y | 2 | 1.5 | 1 |
These are just points you need to plot on a graph: (0, 2) (1, 1.5) and (2,1)
Plot the points then connect the dots to make a line!