Question

determine the initial value and the rate of change of the linear function given in the graph.
(-1, -4/3) (-4, -10/3) they are fractions

Answer 1

determine the initial value and the rate of change of the linear function given in the graph.
(-1, -4/3) (-4, -10/3) they are fractions

A: initial value is 2/3 and the rate of change is -2/3
B: initial value is -2 and the rate of change is 2/3
C: initial value is 1/6 and the rate of change is 3/2
D: initial value is -2/3 and the rate of change is 2/3

Answer 2

determine the initial value and the rate of change of the linear function given in the graph.
(0.5,1) (0,0) (-1.5,3)

A: initial value is 2 and the rate of change is 2
B: initial value is -6 and the rate of change is 2
C: initial value is 0 and the rate of change is 1/2
D: initial value is 0 and the rate of change is 2

Answer 3

To find the initial value and the rate of change of the linear function, first determine the slope of the line using the two points given.

Slope (m) = (y2 - y1) / (x2 - x1)
Slope (m) = ((-10/3) - (-4/3)) / (-4 - (-1))
Slope (m) = (-10/3 + 4/3) / (-4 + 1)
Slope (m) = (-6/3) / (-3)
Slope (m) = -2

Now that we have the slope (rate of change) of the linear function, we can use one of the points to find the initial value (y-intercept). Let's use the first point (-1, -4/3):

y = mx + b
-4/3 = -2(-1) + b
-4/3 = 2 + b

b = -4/3 - 2
b = -10/3

Therefore, the initial value of the linear function is -10/3 and the rate of change is -2.

Answer 4

To find the initial value and rate of change of the linear function, we first need to calculate the slope (rate of change) using the given points:

Slope (m) = (y2 - y1) / (x2 - x1)
Slope (m) = ((-10/3) - (-4/3)) / (-4 - (-1))
Slope (m) = (-10/3 + 4/3) / (-4 + 1)
Slope (m) = (-6/3) / (-3)
Slope (m) = -2/3

Now that we have the slope, we can use one of the points to find the initial value:

Using point (-1, -4/3):
y = mx + b
-4/3 = (-2/3)(-1) + b
-4/3 = 2/3 + b
b = -4/3 - 2/3
b = -6/3
b = -2

Therefore, the initial value is -2 and the rate of change is -2/3. So, the correct answer is:

B: initial value is -2 and the rate of change is -2/3

Answer 5

To determine the initial value and rate of change of the linear function, we need to first calculate the slope using the provided points.

From the points (0.5, 1) and (0, 0):

Slope (m) = (y2 - y1) / (x2 - x1)
Slope (m) = (1 - 0) / (0.5 - 0)
Slope (m) = 1 / 0.5
Slope (m) = 2

So, the rate of change (slope) is 2.

Now, let's find the initial value by substituting the coordinates (0, 0) into the equation of a straight line:

y = mx + b
0 = 2(0) + b
b = 0

Therefore, the initial value is 0 and the rate of change is 2. The correct answer is:

D: initial value is 0 and the rate of change is 2.