Determine the rate of change in the following description. In Ms.
Katy's math class, a homework assignment is worth 100 points.
If students turn the homework in late, there will be a deduction of 5 points per day. (1 point)
O m = 5
The rate of change in this description is -5 points per day.
Use the table to answer the question.
X | У
|
2.6| -6
3.2| 3
Determine the rate of change of the linear function given as a table of values.
To determine the rate of change of a linear function, we need to find the slope of the line connecting the two points provided in the table.
Given the points (2.6, -6) and (3.2, 3), we can calculate the slope using the formula:
slope = (change in y) / (change in x)
The change in y is 3 - (-6) = 9.
The change in x is 3.2 - 2.6 = 0.6.
Plugging these values into the formula, we get:
slope = 9 / 0.6 = 15
Therefore, the rate of change of the linear function given as a table of values is 15.
Find the initial value of the linear function, given that the rate of
change is m=-4/7，and
(14,3) is an (x, y) value of the linear function. (1 point)
To find the initial value of the linear function, we need to apply the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the initial value.
Given that the rate of change is m = -4/7 and (14, 3) is a point on the line, we can substitute these values into the equation:
3 = (-4/7)(14) + b
To solve for b, we can simplify and solve the equation:
3 = -4(2) + b
3 = -8 + b
b = 3 + 8
b = 11
Therefore, the initial value of the linear function is 11.
(0.5,1) (0,0) (-1.5,-3)
Determine the initial value and the rate of change of the linear function as given in the graph.
(1 point
To determine the initial value and rate of change of the linear function, we can use any two points from the graph.
Let's use the points (0.5, 1) and (0, 0).
To find the rate of change (slope), we can use the formula:
slope = (change in y) / (change in x)
The change in y is 1 - 0 = 1.
The change in x is 0.5 - 0 = 0.5.
Plugging these values into the formula, we get:
slope = 1 / 0.5 = 2
Therefore, the rate of change of the linear function is 2.
To find the initial value, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the initial value.
Using the point (0, 0) and the slope of 2, we can substitute these values into the equation and solve for b:
0 = 2(0) + b
0 = 0 + b
b = 0
Therefore, the initial value of the linear function is 0.
The initial value is 2, and the rate of change is 2.
The initial value is 0, and the rate of change is 2.
The initial value is -6,
• and the rate of change is
2
The initial value is 0, and the rate of change is 1/2
My apologies for the confusion. The correct answer is:
The initial value is 0, and the rate of change is 2.
To determine the rate of change in this situation, we need to define the variables and calculate the change.
Let's define:
- H = Homework grade (in points)
- D = Number of days late
Given information:
- A homework assignment is worth 100 points.
- There is a deduction of 5 points per day if turned in late.
The rate of change can be calculated by dividing the change in the dependent variable (H) by the change in the independent variable (D).
In this case, the change in H is the difference between the maximum points (100) and the points deducted for being late (5*D), which can be represented as:
Change in H = 100 - 5*D
The change in D is simply the number of days late, which is D itself.
So, the rate of change can be calculated as:
Rate of change = (Change in H) / (Change in D)
For example, if a student turns in the homework one day late (D = 1), the rate of change would be:
Rate of change = (100 - 5*1) / (1) = 95 / 1 = 95
Therefore, the rate of change in this description is 95 points per day.