Question

for each graph, explain whether the relationship could be proportional.
a
b

Explanation:

Step1: Recall the definition of a proportional relationship

A proportional relationship has a constant ratio between the two variables and passes through the origin \((0,0)\).

Step2: Analyze graph A

Check if the points lie on a straight - line through the origin. The points in graph A seem to lie on a straight line. When the number of bricks is \(0\), the height of the triangular wall is \(0\) (if we assume the trend continues). The ratio of height (in inches) to the number of bricks is constant. For example, if we take two points \((3,4)\) and \((6,8)\), the ratio \(\frac{4}{3}=\frac{8}{6}=\frac{4}{3}\).

Step3: Analyze graph B

Check if the points lie on a straight - line through the origin. The points in graph B do not lie on a straight line. For example, if we consider the points \((3,6)\) and \((6,18)\), the ratio for the first point is \(\frac{6}{3} = 2\), and for the second point \(\frac{18}{6}=3\). Also, if we assume a line of best - fit, it does not pass through the origin \((0,0)\) (since when the number of coins is \(0\), the weight of coins should be \(0\) for a proportional relationship, but the trend of the non - collinear points does not suggest this).

Answer:

Graph A could be proportional. Graph B could not be proportional.