Graph of flower sales over years with a line of best fit to estimate future sales.

Here are the step-by-step solutions for the problems shown.

Problem 10: Flower Sales

A) Graphing the data
To graph this, you need to plot points on the grid.
* X-axis (horizontal): Represents the years since 2007. So, 2007 is $x=0$, 2008 is $x=1$, etc., up to 2012 which is $x=5$.
* Y-axis (vertical): Represents Sales in thousands. The values range from 305 to 420. You should label your vertical axis starting around 300 and going up by increments of 20 or 25 (e.g., 300, 325, 350, 375, 400, 425).

Plot these points:
* $(0, 305)$
* $(1, 330)$
* $(2, 345)$
* $(3, 370)$
* $(4, 395)$
* $(5, 420)$

Draw a straight line that goes through the middle of these dots. It should start near the bottom left and go up towards the top right.

B) Equation for the line of best fit
We need an equation in the form $y = mx + b$.
* $x$ = years since 2007
* $y$ = sales in thousands

Let's find the slope ($m$), which is the rate of change. We can pick two points that look like they are right on the line we drew. Let's use the first point $(0, 305)$ and the last point $(5, 420)$.

$$Slope (m) = \frac{y_2 - y_1}{x_2 - x_1}$$
$$m = \frac{420 - 305}{5 - 0}$$
$$m = \frac{115}{5}$$
$$m = 23$$

So, the sales increase by about $\$23,000$ per year.

Now find the y-intercept ($b$). This is the value of $y$ when $x = 0$. Looking at our data, when $x=0$ (year 2007), $y=305$. So, $b = 305$.

The equation is:
$y = 23x + 305$

*(Note: Depending on exactly how you draw your line, your slope might vary slightly, e.g., 22 or 24, but 23 is the most accurate based on the endpoints).*

C) When will sales reach \$500?
We want to find the year ($x$) when sales ($y$) equal 500. We use the equation from part B.

$$500 = 23x + 305$$

Subtract 305 from both sides:
$$195 = 23x$$

Divide by 23:
$$x \approx 8.48$$

Since $x$ represents years *since* 2007, we add 8.48 to 2007.
$$2007 + 8.48 = 2015.48$$

This means during the year 2015.

***

Problem 11: Test Scores

We need to find the equation of the line passing through the points labeled on the graph: $(7, 65)$ and $(25, 90)$.

Step 1: Find the slope ($m$)
$$m = \frac{y_2 - y_1}{x_2 - x_1}$$
$$m = \frac{90 - 65}{25 - 7}$$
$$m = \frac{25}{18}$$
$$m \approx 1.388...$$

Rounding to one decimal place, the slope is 1.4. This eliminates options C and D immediately because their slopes are 0.72.

Step 2: Find the y-intercept ($b$)
Use the slope $1.4$ and one of the points, for example $(7, 65)$, in the equation $y = mx + b$.

$$65 = 1.4(7) + b$$
$$65 = 9.8 + b$$
$$65 - 9.8 = b$$
$$55.2 = b$$

Rounding to the nearest whole number, $b \approx 55$.

So the equation is $y = 1.4x + 55$.

This matches Option A.

*(Check with Option B just in case: $y = 1.4x - 84$. If we plug in $x=7$, we get $1.4(7) - 84 = 9.8 - 84 = -74.2$. That is definitely not 65, so B is wrong.)*

***

Problem 12: Gym Memberships

Look at the direction of the dots on the scatter plot.
* The horizontal axis (x-axis) is "Cost of a gym membership". As you move to the right, the cost goes up.
* The vertical axis (y-axis) is "Number of new gym memberships sold". As you move down, the number sold goes down.

The dots start high on the left and go low on the right. This means that as the cost goes up, the number sold goes down.

This matches Option B.

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Final Answer:

10.
A) Plot points at coordinates: $(0, 305), (1, 330), (2, 345), (3, 370), (4, 395), (5, 420)$. Draw a straight line through them.
B) $y = 23x + 305$
C) Year 2015 (Calculated by solving $500 = 23x + 305$ to get $x \approx 8.5$, then adding 8.5 years to 2007).

11. A) $y = 1.4x + 55$

12. B) As the cost goes up, the number sold goes down.