9) the scatter plot shows the numbers of drifting scooters sold by a company.
drifting scooter sales
number sold
year
a. in what year were 1,000 scooters sold?
b. about how many scooters were sold in 2019?
c. describe the relationship shown by the data.
d. assuming this trend continues, in what year are about 150 drifting scooters sold?
10) write an equation in slope - intercept form of the line.
(2, 2)
(4, 3)

Question

Accepted Answer

### Question 9
#### Part a
# Explanation:
## Step1: Analyze the scatter plot
Look at the scatter plot where the y - axis is the number of scooters sold and the x - axis is the year. Find the point where the number of scooters sold (y - value) is 1000 and then determine the corresponding year (x - value). From the plot, when the number of scooters sold is 1000, the year is 2018.
# Answer: 2018

#### Part b
# Explanation:
## Step1: Locate the year 2019 on the x - axis
Find the position corresponding to the year 2019 on the scatter plot's x - axis. Then, estimate the y - value (number of scooters sold) at that x - value. From the trend of the scatter plot, the number of scooters sold in 2019 is approximately 900 (or a value close to 900, the initial estimate of 950 is also reasonable as it is an approximation).
# Answer: About 900 (or 950)

#### Part c
# Explanation:
## Step1: Observe the direction of the points
As the year (x - value) increases, the number of scooters sold (y - value) decreases. So, there is a negative correlation between the year and the number of drifting scooters sold. In other words, as the years pass (from 2016 onwards), the number of scooters sold is decreasing.
# Answer: There is a negative relationship (or negative correlation) between the year and the number of drifting scooters sold. As the year increases, the number of scooters sold decreases.

#### Part d
# Explanation:
## Step1: Identify the trend
The trend is a linear decrease (negative slope). First, we can find the rate of decrease. Let's assume the relationship is linear. From the earlier points, for example, from 2016 (let's say x = 2016, y = 1200) to 2018 (x = 2018, y = 1000), the change in x is 2 years and the change in y is - 200. So the slope $m=\frac{\Delta y}{\Delta x}=\frac{1000 - 1200}{2018 - 2016}=\frac{- 200}{2}=- 100$ scooters per year.
## Step2: Set up the linear equation
Let $y=mx + b$, where $y$ is the number of scooters sold, $x$ is the year, $m=- 100$. Using the point (2016, 1200), we can find $b$: $1200=-100\times2016 + b$, $b = 1200+100\times2016=1200 + 201600 = 202800$. So the equation is $y=-100x + 202800$.
## Step3: Solve for x when y = 150
Set $y = 150$ in the equation $150=-100x+202800$. Then, $100x=202800 - 150=202650$, $x=\frac{202650}{100}=2026.5$. So approximately in the year 2027 (since 2026.5 is close to 2027).
# Answer: Approximately 2027

### Question 10
# Explanation:
## Step1: Recall the slope - intercept form
The slope - intercept form of a line is $y=mx + b$, where $m$ is the slope and $b$ is the y - intercept.
## Step2: Calculate the slope ($m$)
We have two points $(2,2)$ and $(4,3)$. The formula for slope $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substituting the values: $m=\frac{3 - 2}{4 - 2}=\frac{1}{2}$.
## Step3: Find the y - intercept ($b$)
Use the point $(2,2)$ and the slope $m = \frac{1}{2}$ in the equation $y=mx + b$. So, $2=\frac{1}{2}\times2 + b$, $2 = 1 + b$, then $b=2 - 1 = 1$.
## Step4: Write the equation
Substitute $m=\frac{1}{2}$ and $b = 1$ into $y=mx + b$. We get $y=\frac{1}{2}x+1$.
# Answer: $y=\frac{1}{2}x + 1$

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QUESTION IMAGE

Question

Explanation:

Question 9

Part a

Step1: Analyze the scatter plot

Step1: Locate the year 2019 on the x - axis

Step1: Observe the direction of the points

Answer:

Part b