Question

1. dillon can bike 6 miles in 0.5 hour. which line has a slope that best represents dillons speed in miles per hour?

Explanation:

Step1: Calculate Dillon's speed

Speed = $\frac{\text{Distance}}{\text{Time}}$. Given distance = 6 miles and time = 0.5 hour. So speed = $\frac{6}{0.5}=12$ miles per hour.

Step2: Analyze slope of a line representing speed

The slope of a line in a distance - time graph is given by $\frac{\Delta y}{\Delta x}$, where $\Delta y$ is the change in distance and $\Delta x$ is the change in time. A slope of 12 means for every 1 - unit increase in time (x - axis), the distance (y - axis) increases by 12 units.

Answer:

The line with a slope of 12 best represents Dillon's speed. In a distance - time graph, if we consider two points $(x_1,y_1)$ and $(x_2,y_2)$ on the line representing Dillon's motion, $\frac{y_2 - y_1}{x_2 - x_1}=12$. For example, if $x_1 = 0,y_1 = 0$ and $x_2=1,y_2 = 12$; or $x_1 = 2,y_1 = 24$ etc.