Question

davids family is taking a road trip to niagara falls. his mom drove the first day, and his dad is driving the second day. his dads entire drive is on the freeway, and he drives at a constant speed without stopping. the graph shows the linear relationship between the time, in hours, davids dad spends driving and the total distance they have driven since leaving home.
complete the equation to model the relationship between the total distance the family has driven, d, and the time davids dad spends driving, t.
d = \square t + \square
complete the sentences to make true statements about the model.
davids dad is driving \square miles per hour. this speed is represented by the \square. the distance davids mom drove is represented by the \square of \square miles.

Explanation:

Step1: Identify the slope (rate of change)

The general form of a linear equation is \( D = mt + b \), where \( m \) is the slope (rate of change) and \( b \) is the y - intercept. To find the slope, we can use two points on the line. From the graph, when \( t = 0 \), \( D=300 \) (this is the y - intercept \( b \)). When \( t = 2 \), \( D = 400 \). The slope \( m=\frac{\Delta D}{\Delta t}=\frac{400 - 300}{2-0}=\frac{100}{2} = 50 \).

Step2: Identify the y - intercept

When \( t = 0 \) (the time David's dad starts driving), the total distance \( D = 300 \) miles. This is the distance that David's mom drove before his dad started driving, so the y - intercept \( b = 300 \).

Step3: Write the equation

Using the slope - intercept form \( D=mt + b \), with \( m = 50 \) and \( b=300 \), the equation is \( D = 50t+300 \).

Step4: Determine the speed

The speed of David's dad is the slope of the line, which is 50 miles per hour. The speed is represented by the slope of the line. The distance David's mom drove is represented by the y - intercept, which is 300 miles.

Answer:

The equation is \( D=\boxed{50}t+\boxed{300} \).
David's dad is driving 50 miles per hour. This speed is represented by the slope. The distance David's mom drove is represented by the y - intercept of 300 miles.