MATH SOLVE

3 months ago

Q:
# Sam is observing the velocity of a car at different times. After two hours, the velocity of the car is 54 km/h. After four hours, the velocity of the car is 58 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.Part B: How can you graph the equation obtained in Part A for the first six hours?

Accepted Solution

A:

Part A, you have 2 points, let x = time and Y = speed,

so you have: (2,54) and (4,58)

find the slope (M):

Y2-y1 / x2-x1:

58-54 / 4-2 = 4/2 = 2

equation for a line = y=Mx+b,

now you have y = 2x+b

using the first point (2,54) solve for b:

54 = 2(2) +b

b = 50

the equation becomes y = 2(x) +50

Part B) since X is the number of hours, replace x with 1, 2,3, 4, 5, and 6 to calculate the corresponding y value, then plot them onto a graph and draw a line through the points.

so you have: (2,54) and (4,58)

find the slope (M):

Y2-y1 / x2-x1:

58-54 / 4-2 = 4/2 = 2

equation for a line = y=Mx+b,

now you have y = 2x+b

using the first point (2,54) solve for b:

54 = 2(2) +b

b = 50

the equation becomes y = 2(x) +50

Part B) since X is the number of hours, replace x with 1, 2,3, 4, 5, and 6 to calculate the corresponding y value, then plot them onto a graph and draw a line through the points.