Determine the initial value and the rate of change of the linear function given in the graph: (2, 3) (0, 0) (1 point) The initial value is , and the rate of change is .

Answer 1

To find the initial value and the rate of change of a linear function, we need to use the formula for the equation of a line:

y = mx + b

where m represents the rate of change (slope) and b represents the initial value (y-intercept).

From the given points (2, 3) and (0, 0), we can use the formula to find the rate of change (m):

m = (y2 - y1) / (x2 - x1)
= (0 - 3) / (0 - 2)
= -3 / -2
= 3/2

Hence, the rate of change is 3/2.

To find the initial value (b), we can substitute the values of one of the given points into the equation and solve for b:

y = mx + b
0 = (3/2)*0 + b
0 = 0 + b
b = 0

Hence, the initial value is 0.

Therefore, the initial value is 0, and the rate of change is 3/2.

Answer 2

Determine the initial value and the rate of change of the linear function given in the graph: (2, 3). (0, 0) (1 point) The initial value is _____ and the rate of change is ______ .

Answer 3

To find the initial value and the rate of change of a linear function, we need to use the formula for the equation of a line:

y = mx + b

where m represents the rate of change (slope) and b represents the initial value (y-intercept).

Using the points (2, 3) and (0, 0), we can find the rate of change (m) as:

m = (y2 - y1) / (x2 - x1)
= (0 - 3) / (0 - 2)
= -3 / -2
= 3/2

Hence, the rate of change is 3/2.

To find the initial value (b), we can substitute the values of one of the given points into the equation and solve for b:

0 = (3/2)*0 + b
0 = 0 + b
b = 0

Hence, the initial value is 0.

Therefore, the initial value is 0 and the rate of change is 3/2.

Answer 4

Determine the initial value and the rate of change of the linear function given in the graph: (-3,2.5), (0,1), and (2, 0) (1 point) The initial value is _______ , and the rate of change is _____ .

Answer 5

To find the initial value and the rate of change of a linear function, we can use the formula for the equation of a line:

y = mx + b

where m represents the rate of change (slope) and b represents the initial value (y-intercept).

Using the points (-3, 2.5), (0, 1), and (2, 0), we can find the rate of change (m) using two of the given points:

m = (y2 - y1) / (x2 - x1)
= (1 - 2.5) / (0 - (-3))
= -1.5 / 3
= -0.5

Hence, the rate of change is -0.5.

To find the initial value (b), we can substitute any of the points into the equation and solve for b. Let's use the point (0, 1):

1 = -0.5 * 0 + b
1 = b

Hence, the initial value is 1.

Therefore, the initial value is 1, and the rate of change is -0.5.

Answer 6

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) Responses A. m=100 B. m = -100 C. m = 5. D. m = -5

Answer 7

The rate of change in this scenario is determined by the deduction of points for turning in the homework late. From the given information, we know that there will be a deduction of 5 points per day.

Since the deduction is of 5 points per day, it means that for every day the homework is turned in late, the student loses 5 points. This loss of points is a decrease, which indicates a negative rate of change.

Therefore, the correct response is:
D. m = -5

Answer 8

The Kims are hosting a catered dinner. The cost for 3 servings is $18. The cost for 10 servings is $60. What is the cost per serving?(1 point) $ _____ per serving

Answer 9

To find the cost per serving, we need to determine the rate of change in the cost based on the number of servings. We can use the formula for the equation of a line:

y = mx + b

where y represents the cost and x represents the number of servings.

Using the given points (3, 18) and (10, 60), we can find the rate of change (m):

m = (y2 - y1) / (x2 - x1)
= (60 - 18) / (10 - 3)
= 42 / 7
= 6

Hence, the rate of change is 6.

To find the cost per serving, we need to substitute the values of one of the given points into the equation and solve for y:

18 = 6*3 + b
18 = 18 + b
b = 0

Hence, the initial value is 0.

Therefore, the equation for the cost per serving is:

y = 6x + 0

Since the rate of change (m) corresponds to the coefficient of x, the cost per serving is $6 per serving.