Question

use the graph to write an equation of the line. distance traveled (graph: y - axis labeled distance (miles), x - axis labeled time (hours), line passing through (0, 0) and (3, 165))
y =
interpret the slope.

Explanation:

Step1: Find the slope (rate of change)

The line passes through the origin \((0,0)\) and \((3,165)\). The slope \(m\) is calculated as \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Substituting the points \((0,0)\) and \((3,165)\), we get \(m=\frac{165 - 0}{3 - 0}=\frac{165}{3} = 55\).

Step2: Write the equation of the line

Since the line passes through the origin, the y - intercept \(b = 0\). The slope - intercept form of a line is \(y=mx + b\). Substituting \(m = 55\) and \(b = 0\) into the formula, we get \(y = 55x\).

Answer:

For the equation of the line: \(y=\boldsymbol{55x}\)

For the interpretation of the slope: The slope of 55 means that the distance traveled (in miles) increases by 55 miles for each hour of time elapsed. In other words, the speed is 55 miles per hour.