The correct answer is:
Initial value: 4, rate of change: negative 3 over 4.
Identify the initial value and rate of change for the graph shown. (4 points)
A coordinate plane graph is shown. A line is graphed that passes through the y-intercept at 4 and through the point 4 comma 1.
Initial value: 5.5, rate of change: negative 3 over 4.
Initial value: 4, rate of change: negative 3 over 4.
Initial value: negative 3 over 4., rate of change: 4
Initial value: negative 3 over 4., rate of change: 5.5
5 answers
What is the rate of change and initial value for the linear relation that includes the points shown in the table? (4 points)
x y
2 3
4 5
6 7
8 9
Initial value: 1, rate of change: 2
Initial value: 1, rate of change: 1
Initial value: 2, rate of change: 2
Initial value: 3, rate of change: 2
x y
2 3
4 5
6 7
8 9
Initial value: 1, rate of change: 2
Initial value: 1, rate of change: 1
Initial value: 2, rate of change: 2
Initial value: 3, rate of change: 2
To find the rate of change, we can calculate the difference in y-values divided by the difference in x-values between any two points:
For the points (2, 3) and (4, 5):
Rate of change = (5 - 3) / (4 - 2) = 2 / 2 = 1
Hence, the rate of change is 1.
To find the initial value, we can substitute any point into the slope-intercept form of a linear equation (y = mx + b) and solve for the initial value (b):
Using the point (2, 3):
3 = 1(2) + b
3 = 2 + b
b = 3 - 2
b = 1
Hence, the initial value is 1.
Therefore, the correct answer is:
Initial value: 1, rate of change: 1.
For the points (2, 3) and (4, 5):
Rate of change = (5 - 3) / (4 - 2) = 2 / 2 = 1
Hence, the rate of change is 1.
To find the initial value, we can substitute any point into the slope-intercept form of a linear equation (y = mx + b) and solve for the initial value (b):
Using the point (2, 3):
3 = 1(2) + b
3 = 2 + b
b = 3 - 2
b = 1
Hence, the initial value is 1.
Therefore, the correct answer is:
Initial value: 1, rate of change: 1.
A delivery truck has 40,000 miles on its odometer and travels an average of 22,000 miles per year.
Which function best models the linear relationship? (4 points)
y = 22,000x - 40,000
y = −22,000x + 40,000
y = 22,000x + 40,000
y = 40,000x - 22,000
Which function best models the linear relationship? (4 points)
y = 22,000x - 40,000
y = −22,000x + 40,000
y = 22,000x + 40,000
y = 40,000x - 22,000
The function that best models the linear relationship is:
y = 22,000x + 40,000.
In this equation, x represents the number of years and y represents the total number of miles on the odometer. The initial value is 40,000 miles (the starting point on the odometer) and the rate of change is 22,000 miles per year (the average number of miles travelled each year).
y = 22,000x + 40,000.
In this equation, x represents the number of years and y represents the total number of miles on the odometer. The initial value is 40,000 miles (the starting point on the odometer) and the rate of change is 22,000 miles per year (the average number of miles travelled each year).
1 answer