Which graph represents a proportional relationship? On a coordinate plane, a straight line with negative slope goes through points (2, 6), (4, 5). On a coordinate plane, a curve opens down. On a coordinate plane, a straight line with positive slope goes through points (5, 2) and (6, 3). On a coordinate plane, a straight line with positive slope goes through points (3, 3) and (4, 4).

D. On a coordinate plane, a straight line with positive slope goes through points (3, 3) and (4, 4).

Explanation:

For a relationship to be proportional it needs to meet two conditions:

1) its graph needs to be a straight line

2) every point of the graph needs to satisty the equation y = k•x, or, in other words k has to be equal for every point

Now, let's check the answers;

A) we have two points: A (2, 6) and B (4, 5). For point A, x is 2 and y is 6, so:

y = k•x

6 = k•2

k = 3

For point B, x is 4 and y is 5, so:

y = k•x

5 = k•4

k= 5/4

Since k isn't the same value for these two points, this isn't proprtional relationship.

B) this graph is curve, so since it's not a straight line it can't be proportional relationship.

C) similarly to graph A we have point A (5, 2) and point B (6, 3).

For point A, x is 5 and y is 2, so:

y = k•x

2 = k•5

k = 2/5

For point B, x is 6 and y is 3, so:

y = k•x

3 = k•6

k = 1/2

Again values of k aren't the same, so this isn't a proportional relationship.

D) Point A (3, 3) and point B (4, 4). For point A, x is 3 and y is 3, so:

y = k•x

3 = k•3

k = 1

For point B, x is 4 and y is 4, so:

y = k•x

4 = k•4

k = 1

Since value of k is the same for both points, this graph shows the proportional relationship.

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