Graphing Lines by Plotting Points Examples

Graph the equation y = -0.5x – 2.

How about this: we'll pick some values for x and solve for y, since y is already isolated.

x	y = -0.5x – 2	(x, y)
	y = -0.5(0) – 2 y = 0 – 2 y = -2	(0, -2)
1	y = -0.5(1) – 2 y = -0.5 – 2 y = -2.5	(1, -2.5)
2	y = -0.5(2) – 2 y = -1 – 2 y = -3	(2, -3)

Now let's plot them and connect them:

Graph the equation 2y = 6x.

Let's solve this one for y.

	divide both sides by 2
	simplify

Now, let's plug in some numbers for x and solve for y.

x	y = 3x	(x, y)
	y = 3(0) y = 0	(0, 0)
1	y = 3(1) y = 3	(1, 3)
-1	y = 3(-1) y = -3	(-1, -3)

Plot and connect.

Which equation matches the following graph?

a. y = 3x + 1
b. y = x + 3
c. y = 3x – 1
d. y = -3x + 1

We can see that the point (-1, 4) is right there on the line, so this point must be a solution to the equation. We can test each equation and see which one is true for x = -1 and y = 4. It's a plug-and-chug problem.

Plugging x = -1 into the first equation, we get y = 3(-1) + 1 = -2, which is not equal to 4. Bzzt, that's not the answer.

Plugging x = -1 into the second equation, we get y = -1 + 3 = 2. Nope, it's not equal to 4 either.

Next up, we plug x = -1 into the third equation to get y = 3(-1) – 1 = -4. Close, but that's still not equal to positive 4.

Fourth time's a charm. Throw x = -1 into the last equation and we get y = -3(-1) + 1 = 4. This gives us the solution (-1, 4), so it's the correct equation.