Which of the following shows the graph of a line through (-2,2) and (2,4)

You didn't include the options, but one and only one line passes through two poins.

You can find the equation of the line that passes through two known points in this way:

[Y -Y1] / [X -X1] = [Y2 - Y1] / [X2 -X1]

in this case (X1,Y1) = (-2,2) and (X2,Y2) = (2,4)

=> [Y - (2) ] / [X - (-2) ] = [4 - 2] / [2 - (-2) ]

=> [Y -2] / [X + 2] = 2/4 = 1/2

=> 2 * (Y - 2)  = X + 2

=> 2Y - 4 = X + 2

=> 2Y = X + 2 + 4

=> 2y = x + 6

=> y = x/2 + 3

So you must look the graph of that equation.

Some of the points of that graph are:

x         y

-6       -6/2 + 3 = 0

-4        -4/2 + 3 = 1

-2         -2/2 + 3 = 2

0           0 + 3 = 3

2           2/2 + 3 = 4

4           4/2 + 3 = 5

So, you should find the correspondant graph easily.

Attachment for graph.

Step-by-step explanation:

Given: (-2,2) and (2,4)

Two points are given and to find the equation of line passing through the points.

First we find the slope of the line.

              

Point: (2,4)

using point slope form:

Now, we draw the graph using two given points. Plot the points on graph and join them.

Please find the attachment for graph.