Question
The cost of Candy Bar A is displayed in the table. The proportional relationship between the cost and quantity for Candy Bar B is represented by the equation y = x. Which candy bar is the cheapest cost per bar?
$ Cost of Candy Bar A
Quantity/Cost
(1) (1.25)
(2) (2.50)
(3) (3.75)
(4) (5.00)
(5) (6.25)
Enter 1 for Candy Bar A. Enter 2 for Candy Bar B.
$ Cost of Candy Bar A
Quantity/Cost
(1) (1.25)
(2) (2.50)
(3) (3.75)
(4) (5.00)
(5) (6.25)
Enter 1 for Candy Bar A. Enter 2 for Candy Bar B.
Answers
Answer
Write y - 6x = 5 in slope-intercept form
Answer
Graph the equation x - y = 6 using the form y = mx + b
Answered by
GPT-4o mini
To determine which candy bar is cheaper per bar, we need to find the cost per unit for Candy Bar A and Candy Bar B.
For Candy Bar A, based on the provided data:
- When the quantity is 1, the cost is $1.25, which gives a cost per bar of $1.25.
- When the quantity is 2, the cost is $2.50, which gives a cost per bar of $1.25.
- When the quantity is 3, the cost is $3.75, which gives a cost per bar of $1.25.
- When the quantity is 4, the cost is $5.00, which gives a cost per bar of $1.25.
- When the quantity is 5, the cost is $6.25, which gives a cost per bar of $1.25.
Thus, the cost per bar for Candy Bar A is consistently $1.25.
For Candy Bar B, the equation is y = x, which means the cost per bar is $1.00 for each bar, regardless of the quantity.
Now, let's compare the costs:
- Candy Bar A: $1.25 per bar
- Candy Bar B: $1.00 per bar
Since $1.00 (Candy Bar B) is less than $1.25 (Candy Bar A), **Candy Bar B is the cheaper option**.
Therefore, the answer is:
**Enter 2 for Candy Bar B.**
For Candy Bar A, based on the provided data:
- When the quantity is 1, the cost is $1.25, which gives a cost per bar of $1.25.
- When the quantity is 2, the cost is $2.50, which gives a cost per bar of $1.25.
- When the quantity is 3, the cost is $3.75, which gives a cost per bar of $1.25.
- When the quantity is 4, the cost is $5.00, which gives a cost per bar of $1.25.
- When the quantity is 5, the cost is $6.25, which gives a cost per bar of $1.25.
Thus, the cost per bar for Candy Bar A is consistently $1.25.
For Candy Bar B, the equation is y = x, which means the cost per bar is $1.00 for each bar, regardless of the quantity.
Now, let's compare the costs:
- Candy Bar A: $1.25 per bar
- Candy Bar B: $1.00 per bar
Since $1.00 (Candy Bar B) is less than $1.25 (Candy Bar A), **Candy Bar B is the cheaper option**.
Therefore, the answer is:
**Enter 2 for Candy Bar B.**
Answered by
GPT-4o mini
To convert the equation \( y - 6x = 5 \) into slope-intercept form, we want to isolate \( y \) on one side of the equation. The slope-intercept form of a line is given by the equation \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
Starting with the original equation:
\[
y - 6x = 5
\]
Add \( 6x \) to both sides to isolate \( y \):
\[
y = 6x + 5
\]
Now, the equation is in slope-intercept form, where:
- The slope \( m \) is \( 6 \),
- The y-intercept \( b \) is \( 5 \).
Thus, the slope-intercept form of the equation is:
\[
y = 6x + 5
\]
Starting with the original equation:
\[
y - 6x = 5
\]
Add \( 6x \) to both sides to isolate \( y \):
\[
y = 6x + 5
\]
Now, the equation is in slope-intercept form, where:
- The slope \( m \) is \( 6 \),
- The y-intercept \( b \) is \( 5 \).
Thus, the slope-intercept form of the equation is:
\[
y = 6x + 5
\]
Answered by
GPT-4o mini
To graph the equation \( x - y = 6 \) using the slope-intercept form \( y = mx + b \), we first need to convert it into that form.
Starting with the equation:
\[
x - y = 6
\]
We want to isolate \( y \). To do this, we can rearrange the equation:
1. Subtract \( x \) from both sides:
\[
-y = -x + 6
\]
2. Now, multiply by -1 to solve for \( y \):
\[
y = x - 6
\]
Now, we have the equation in slope-intercept form \( y = mx + b \), where:
- The slope \( m \) is \( 1 \).
- The y-intercept \( b \) is \( -6 \).
### Steps to Graph the Equation:
1. **Plot the y-intercept**: Start at the y-intercept (0, -6) and plot this point on the graph.
2. **Use the slope**: The slope \( m = 1 \) means that for every 1 unit you move up (rise), you move 1 unit to the right (run). From the point (0, -6), you can:
- Move up 1 unit to (1, -5) and then move right 1 unit to (1, -5).
3. **Plot additional points**: Continuing from (1, -5):
- Move up 1 unit to (2, -4) and then right 1 unit to (2, -4).
4. **Draw the line**: Connect your plotted points with a straight line.
### Key Points:
- **Y-intercept**: (0, -6)
- **Additional points**: (1, -5) and (2, -4)
Your graph will represent the equation \( x - y = 6 \) as a straight line with a slope of 1, and it crosses the y-axis at -6.
Starting with the equation:
\[
x - y = 6
\]
We want to isolate \( y \). To do this, we can rearrange the equation:
1. Subtract \( x \) from both sides:
\[
-y = -x + 6
\]
2. Now, multiply by -1 to solve for \( y \):
\[
y = x - 6
\]
Now, we have the equation in slope-intercept form \( y = mx + b \), where:
- The slope \( m \) is \( 1 \).
- The y-intercept \( b \) is \( -6 \).
### Steps to Graph the Equation:
1. **Plot the y-intercept**: Start at the y-intercept (0, -6) and plot this point on the graph.
2. **Use the slope**: The slope \( m = 1 \) means that for every 1 unit you move up (rise), you move 1 unit to the right (run). From the point (0, -6), you can:
- Move up 1 unit to (1, -5) and then move right 1 unit to (1, -5).
3. **Plot additional points**: Continuing from (1, -5):
- Move up 1 unit to (2, -4) and then right 1 unit to (2, -4).
4. **Draw the line**: Connect your plotted points with a straight line.
### Key Points:
- **Y-intercept**: (0, -6)
- **Additional points**: (1, -5) and (2, -4)
Your graph will represent the equation \( x - y = 6 \) as a straight line with a slope of 1, and it crosses the y-axis at -6.
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