Malia is observing the velocity of a cyclist at different times. After two hours, the velocity of the cyclist is 15 km/h. After five hours, the velocity of the cyclist is 12 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. Part B How can you graph the equations obtained in Part A for the first 12 hours?
you have two points: (2,15) and (5,12)
the line between them has slope -1, so the equation is
v(t) = -1(t-2) + 15 = 17-t
wtf
Part A: To write an equation in two variables to describe the velocity of the cyclist at different times, we can use the slope-intercept form of an equation, y = mx + b. In this case, y represents the velocity of the cyclist, x represents the time in hours, m represents the slope of the line, and b represents the y-intercept.
Let's define the variables:
- y: Velocity of the cyclist (in km/h)
- x: Time (in hours)
- m: Slope of the line (change in velocity over change in time)
- b: Y-intercept (velocity when the time is zero)
To find the slope (m), we can use the formula:
m = (change in y) / (change in x)
Given two points, (2, 15) and (5, 12), we can calculate the slope as follows:
m = (12 - 15) / (5 - 2)
m = -3 / 3
m = -1
Now, we can plug the values of m and one of the given points (2, 15) into the slope-intercept equation to find the y-intercept (b):
15 = -1 * 2 + b
15 = -2 + b
b = 17
Therefore, our equation in standard form to describe the velocity of the cyclist is:
y = -x + 17
Part B: To graph the equation obtained in Part A for the first 12 hours, we can create a chart showing the time (x) on the x-axis and the velocity (y) on the y-axis.
1. Determine the range of values for the x-axis. In this case, we want to graph for the first 12 hours, so the x-axis should range from 0 to 12.
2. Plot points on the graph using the equation y = -x + 17. Choose a few x-values within the range determined in step 1, and calculate the corresponding y-values:
- For x = 0, y = -0 + 17 = 17
- For x = 2, y = -2 + 17 = 15
- For x = 5, y = -5 + 17 = 12
- For x = 12, y = -12 + 17 = 5
3. Plot the points (0, 17), (2, 15), (5, 12), and (12, 5) on the graph.
4. Connect the plotted points with a straight line. Since the equation describes a linear relationship, the graph will be a straight line.
The resulting graph should show the velocity of the cyclist at different times for the first 12 hours, with time on the x-axis and velocity on the y-axis.