Slope of the line is 3/6 or 1/2.
Based on the given information, the relationship between the number of quarts of blue paint (z) and the number of quarts of yellow paint (y) is represented by the graph.
To find the constant of proportionality as shown in the graph, we need to determine the slope of the line.
The slope represents the rate at which the blue paint and yellow paint are being mixed. In this case, the slope will give us the amount of blue paint (z) needed for each quart of yellow paint (y).
We can find the slope by selecting two points on the line and using the formula:
slope = (change in y)/(change in z)
Let's choose two points on the line, for example:
Point 1: (0 quarts of blue paint, 0 quarts of yellow paint)
Point 2: (6 quarts of blue paint, 3 quarts of yellow paint)
Now, let's calculate the slope:
slope = (3 quarts of yellow paint - 0 quarts of yellow paint) / (6 quarts of blue paint - 0 quarts of blue paint)
= 3/6
= 1/2.