Question

what is the slope of the line?
the chart shows the relationship between distance (mi) and time (h). the x - axis represents time (h) with values 0, 1, 2, 3, 4, and the y - axis represents distance (mi) with values 0, 50, 100, 150, 200. the line passes through the origin (0,0) and other points like (1,50), (2,100), (3,150), (4,200) approximately.

Explanation:

Step1: Recall slope formula

The slope \( m \) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \).

Step2: Identify two points on the line

From the graph, the line passes through \((0, 0)\) and \((1, 50)\) (we can also use other points like \((2, 100)\), \((3, 150)\), etc.). Let \((x_1, y_1)=(0, 0)\) and \((x_2, y_2)=(1, 50)\).

Step3: Calculate the slope

Substitute the values into the slope formula: \( m=\frac{50 - 0}{1 - 0}=\frac{50}{1} = 50 \).

Answer:

50