Question

Identify the initial value and rate of change for the graph shown. 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 Question 2(Multiple Choice Worth 4 points) (05.03) 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? y = 22,000x − 40,000 y = –22,000x + 40,000 y = 22,000x + 40,000 y = 40,000x − 22,000 Question 3(Multiple Choice Worth 4 points) (05.03) Karma baked 48 cookies yesterday. Every hour, she bakes another batch of 12 cookies. What is the rate of change for the scenario described? 4 12 60 48 Question 4(Multiple Choice Worth 4 points) (05.03) What is the rate of change and initial value for the linear relation that includes the points shown in the table? x y 1 10 2 8 3 6 4 4 Initial value: 12, rate of change: −2 Initial value: 8, rate of change: 2 Initial value: 12, rate of change: 2 Initial value 8, rate of change: −2 Question 5(Multiple Choice Worth 4 points) (05.03) Cory's roses grow around 1 inch each month. When he planted them they were 6 inches tall. What is the initial value for the scenario described? 0 1 6 12

Answer 1

y int at (0,4).....thru points (4,1)
slope = (1 - 4) / (4 - 0) = -3/4
initial value 4, slope(rate of change) is -3/4 <==
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y = 22,000x + 40,000
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y = 12x + 48
slope(rate of change) = 12
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(1,10)(2,8)
slope = (8-10) / (2-1) = -2/1 = -2

y = mx + b
8 = -2(2) + b
8 = -4 + b
8 + 4 = b
12 = b

slope(rate of change) = -2
initial value = 12
I am not getting any of ur answer choices ...
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y = x + 6
initial value = 6

Answer 2

Following are the calculation of the initial value and rate of change for the graph:

Calculating the point:

When y points at $(0,4)$ thru points $(4,1)$

$(0, 4)\ (4,1) \\\\\to x_1= 0\\\\\to x_2=4\\\\\to y_1= 4\\\\\to y_2=1$

calculating the slope by using the slope formula:

$\to m=\frac{y_2-y_1}{x_2-x_1}$

        $=\frac{1-4}{4-0}\\\\=\frac{-3}{4}\\\\= - \frac{3}{4}$

So, the initial value $4$, and the slope(rate of change) is $-\frac{3}{4}$

$\to y = 22,000x + 40,000 \\\\\to y = 12x + 48$

Therefore, the rate of change (slope) $= 12$

Points:

$(1,10)\ (2,8)$

$\to x_1= 1\\\\\to x_2=2\\\\\to y_1= 10\\\\\to y_2=8$

calculating the slope by using the slope formula:

$\to m=\frac{y_2-y_1}{x_2-x_1}$

       $= \frac{(8-10)}{(2-1)} \\\\= -\frac{2}{1}\\\\ = -2$

Using the formula for calculating the standard line:

$\to y = mx + b\\\\\to 8 = -2(2) + b \\\\\to 8 = -4 + b \\\\\to 8 + 4 = b\\\\\to 12 = b$

So, the rate of change (slope) $= -2$ , and initial value $= 12$

Therefore,  the final answer is "$y = x + 6$", and the  initial value $= 6$

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