Question

Marion is observing the velocity of a cyclist at different times. After two hours, the velocity of the cyclist is 18 km/h. After four hours, the velocity of the cyclist is 4 km/h.

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

Part B: How can you graph the equations obtained in Part A for the first 8 hours? (5 points)

Answer 1

Part A:
Express the given number of hours and velocities of the cyclist as ordered pairs. The time (number of hours) can be our abscissa (x-coordinate) and the velocities can be our ordinate (y-coordinate). The coordinates are therefore (2, 18) and (4, 4). The equation that can be formed in this is established through the two-point equation.

(y - y₁) = ((y₂ - y₁)/(x₂ - x₁))(x - x₁)

Substitute the known variables.
(y - 18) = ((4 - 18)/(4 - 2))(x - 2)

Simplifying the equation,
y - 18 = -7(x - 2)
y = -7x + 32

ANSWER: y = -7x + 32

Part B: This can be graph in the Cartesian plane and numbers 1 to 8 can be substituted to y and take note of the ordered pairs for each point. The slope of the line should be -7 and the y-intercept is 32.