Question

camila is going to drive from her house to city a without stopping. let d represent camilas distance from city a t hours after leaving her house. a graph of d is shown below. write an equation for d then state the slope of the graph and determine its interpretation in the context of the problem.

Explanation:

Step1: Find two points on the line

From the graph, when \(t = 0\), \(D=280\) (the \(y\) - intercept, \(b = 280\)). Let's assume another point. If we assume the line passes through \((8,0)\)

Step2: Calculate the slope \(m\)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Using \((x_1,y_1)=(0,280)\) and \((x_2,y_2)=(8,0)\)

$$m=\frac{0 - 280}{8-0}=\frac{- 280}{8}=-35$$

Step3: Write the equation of the line

The slope - intercept form of a line is \(D=mt + b\). Substituting \(m=-35\) and \(b = 280\)

$$D=-35t + 280$$

Step4: Interpret the slope

The slope \(m=-35\). In the context of the problem, since \(D\) is the distance from City A and \(t\) is the time in hours. The slope represents the rate of change of the distance from City A with respect to time.

Answer:

The equation for \(D\) is \(D=-35t + 280\). The slope of the graph is \(-35\), which means that Camila's distance from City A decreases by 35 miles per hour.