Question

1. the points (15, 21) and (25, 35) form a proportional relationship. a. find the slope of the line that passes through these points. b. which graph represents this relationship?

Explanation:

Step1: Recall slope - formula

The slope formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Given $(x_1,y_1)=(15,21)$ and $(x_2,y_2)=(25,35)$.

Step2: Substitute values into formula

$m=\frac{35 - 21}{25 - 15}=\frac{14}{10}=\frac{7}{5}=1.4$.

Step3: Analyze proportional - relationship and graph

A proportional relationship has the form $y = mx$ and passes through the origin $(0,0)$. Since the slope $m = 1.4>0$, the line should have a positive slope. Looking at the graphs, we need to find a graph with a positive - sloped line passing through the origin (because of the proportional relationship).

Answer:

a. The slope is $\frac{7}{5}$ or $1.4$.
b. Without seeing the full - details of the graphs (but knowing the slope is positive and the line should pass through the origin for a proportional relationship), we need to look for a graph with a positive - sloped line starting from the origin. If we assume the standard orientation of the $x$ and $y$ axes (where $x$ is horizontal and $y$ is vertical), the graph with a positive slope starting from the origin would be the correct one.