graph the proportional relationship y = 2x by plotting points

Answer 1

To graph the proportional relationship y = 2x, we can pick some values of x and calculate the corresponding values of y.

Let's choose the following values of x: -3, -2, -1, 0, 1, 2, 3.

When x = -3, y = 2(-3) = -6
When x = -2, y = 2(-2) = -4
When x = -1, y = 2(-1) = -2
When x = 0, y = 2(0) = 0
When x = 1, y = 2(1) = 2
When x = 2, y = 2(2) = 4
When x = 3, y = 2(3) = 6

Plotting these points on a graph, we get the following graph of the proportional relationship y = 2x:

(3, 6)
(2, 4)
(1, 2)
(0, 0)
(-1, -2)
(-2, -4)
(-3, -6)

As you can see, the points lie on a straight line that passes through the origin (0,0) with a slope of 2. This is because the relationship y = 2x is a proportional relationship, where y is always twice the value of x.