**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!

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