Question

Sam is observing the velocity of a car at different times. After three hours, the velocity of the car is 51 km/h. After five hours, the velocity of the car is 59 km/h.

Part A: Write an equation in two variables in the standard form that can be used to describe the velocity of the car at different times. Show your work and define the variables used. (5 points)

Part B: How can you graph the equation obtained in Part A for the first six hours? (5 points)

Answer 1

It's not obvious here, but you're being asked to find a linear equation for the velocity of the car, given two points on the line that represents this velocity.

Find the slope of the line segment that connects the points (3 hr, 51 km/hr) and (5 hr, 59 km/hr). Graph this line. Where does this line intersect the y-axis? Find the y-value; it's your "y-intercept," b.

Now write the equation: velocity = (slope of line)*t + b

The units of measurement of "slope of line" must be "km per hour squared," and those of the "y-intercept" must be "km per hour."

Part B: Start with the y-intercept (calculated above). Plot it on the vertical axis of your graph. Now label the horizontal axis in hours: {0, 1, 2, 3, 4, 5, 6}. Draw a vertical line through t=6 hours. It will intercept both the horiz. axis and the sloping line representing the velocity as a function of time. Show only the part of the graph that extends from t=0 hours to t=6 hours.