You are an entrepreneur selling handmade kites. Your company Kites-R-Fun has been contacted by a customer in Alaska who wants to purchase several of your best-selling kites and wants you to ship them to her.

Question

🪁You charge $6 per kite plus a flat rate (one-time) of $10 to ship these items to Alaska.

Write an equation for the total cost, `y`, in terms of the number of kites purchased `x`:

Answer 1

To determine the total cost \( y \) in terms of the number of kites purchased \( x \), we need to consider both the cost of the kites and the shipping fee.

1. The cost per kite is $6, so for \( x \) kites, the total cost for the kites is \( 6x \).
2. There is a flat shipping rate of $10.

Combining these two components, the equation for the total cost \( y \) can be expressed as:

\[ y = 6x + 10 \]

This equation reflects the total cost of purchasing \( x \) kites, including the shipping fee.

Answer 2

The customer is comparing prices with your competition!

🪁Your competitor, Windy Kites, sells the same kites, but charges $4 per kite. They charge a flat rate (one-time) of $16 for shipping.

Write an equation for the total cost, `y`, in terms of the number of kites purchased `x`:

Answer 3

For the competitor Windy Kites, we can similarly break down the total cost \( y \) in terms of the number of kites purchased \( x \).

1. Windy Kites charges $4 per kite, so for \( x \) kites, the total cost for the kites is \( 4x \).
2. They also have a flat shipping fee of $16.

Combining these two components, the equation for the total cost \( y \) for Windy Kites can be expressed as:

\[ y = 4x + 16 \]

This equation represents the total cost of purchasing \( x \) kites from Windy Kites, including their shipping fee.

Answer 4

Graph y\ =\ \frac{1}{2}x-1

Answer 5

To graph the equation \( y = \frac{1}{2}x - 1 \), follow these steps:

1. Identify the y-intercept: The equation is in slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. Here, the y-intercept is \( b = -1 \). This means the graph will cross the y-axis at the point \( (0, -1) \).

2. Identify the slope: The slope \( m \) is \( \frac{1}{2} \). This means that for every 1 unit you move vertically (up), you move 2 units horizontally (to the right).

3. Plot the y-intercept: Start by plotting the point \( (0, -1) \) on the graph.

4. Use the slope to find another point:

   • From \( (0, -1) \), move up 1 unit (to \( y = 0 \)) and right 2 units (to \( x = 2 \)). This gives you the point \( (2, 0) \).
   • Alternatively, you could find another point by moving down 1 unit (to \( y = -2 \)) and left 2 units (to \( x = -2 \)). This gives you the point \( (-2, -2) \).

5. Draw the line: Once you have at least two points, draw a straight line through these points extending in both directions.

Here's a basic representation of the graph:

 y
 |
3|          .                  
2|        .
1|      .
0|.......
-1|.  
-2|  .
-3|                              
   |------------------- x
    -3  -2  -1  0  1  2  3

Key Points:

• The graph crosses the y-axis at \( (0, -1) \).
• It has a positive slope, indicating that the line rises as you move from left to right.
• The line continues infinitely in both directions.