Use the table to answer the question.

Question

No. of Units Sold (x) 0 10 20
Profits (y) −160 −97 −34
A company’s monthly profits are represented in the data table. Use the table to derive an equation to determine profits. How many units will the company need to sell in order to make a profit? Provide the answer as a whole number.

Hint: Start by finding the number of units needed such that the profits are equal to zero. If the value is a decimal, then round up to the next whole number, and that is the number of units needed to make a profit. If the value is a whole number, add one unit to find the value needed.

(1 point)
The number of units sold for the company to make a profit is
units.

Answer 1

To derive the equation for profits based on the data provided, we can first establish the relationship between units sold (x) and profits (y) by determining the slope of the line that connects the given points.

We have the following points based on the data:

• Point 1: (0, -160)
• Point 2: (10, -97)
• Point 3: (20, -34)

To find the slope (m), we can use the formula:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Using points (0, -160) and (10, -97):

\[ m = \frac{-97 - (-160)}{10 - 0} = \frac{-97 + 160}{10} = \frac{63}{10} = 6.3 \]

Now, we can use one of the points to derive the equation of the line in the slope-intercept form, \(y = mx + b\). Let's use the point (0, -160):

The equation becomes:

\[ y = 6.3x - 160 \]

Now, we want to find the number of units sold (x) when profits (y) are equal to zero:

\[ 0 = 6.3x - 160 \]

Now, we solve for \(x\):

\[ 6.3x = 160 \ x = \frac{160}{6.3} \approx 25.3968254 \]

Since we need a whole number and per the hint provided, we round up because this is not a whole number. Therefore, \(x\) would round to 26.

So, the number of units sold for the company to make a profit is:

26 units.