Question

Sam is observing the velocity of a car at different times. After three hours, the velocity of the car is 53 km/h. After six hours, the velocity of the car is 62 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 seven hours? (5 points)

Answer 1

In six hours, the car has increased in a velocity of 9 km/h. If your x-axis is time in hours, and your y-axis is the distance in km, you can make two points: (3, 53) and (6, 62). Using this, you can find both the slope and the y-intercept, where x=0

Use the formula for slope: rise/ run --> x2-x1/y2-y1
So, you would do: 6-3/62-53
That simplifies to 1/3, so that's your slope.

Plug this into y - k = m (x - h), where (h, k) is a given point.
You can use either (3, 53) or (6, 62) at this point.

y - 53 = 1/3 (x-3)
y - 53 = (1/3)(x) + (1/3)(-3)
y - 53 = (1/3)x -1
y = (1/3)x +52
This is your simplified equation.