SOLUTION: what are the 2 points and slope for this question ? Connor uses a gift card to buy milkshakes for himself and his friends Thursday after he and a friend order the balance on Konn

Question 1198769: what are the 2 points and slope for this question ?
Connor uses a gift card to buy milkshakes for himself and his friends Thursday after he and a friend order the balance on Konners gift card was $22.45 Saturday after he and four friends ordered he had a balance of $6.70 on his card determine the cost of each milkshake.
I need help finding
1 . 2 points
2. rate of change or slope
3. Dependent variable
4 independent variable.
Answer by textot(100) (Show Source): You can put this solution on YOUR website!
To analyze the situation mathematically, we can represent it as a linear relationship where the balance on the gift card decreases as the number of milkshakes purchased increases.
---
### Step 1: Define Variables
- **Independent Variable**: The number of milkshakes ordered (denoted as $ x $).
- **Dependent Variable**: The remaining balance on the gift card (denoted as $ y $).
---
### Step 2: Identify Two Points
We are given:
1. After Connor and one friend (2 milkshakes) ordered, the balance was $22.45. This gives the point $(2, 22.45)$.
2. After Connor and four friends (5 milkshakes) ordered, the balance was $6.70. This gives the point $(5, 6.70)$.
---
### Step 3: Find the Rate of Change (Slope)
The slope represents the rate at which the balance decreases per milkshake:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substitute the points $(2, 22.45)$ and $(5, 6.70)$:
\[
m = \frac{6.70 - 22.45}{5 - 2} = \frac{-15.75}{3} = -5.25
\]
The slope is $ -5.25 $, meaning each milkshake costs **$5.25**.
---
### Step 4: Equation of the Line
Using the point-slope form:
\[
y - y_1 = m(x - x_1)
\]
Substitute $ m = -5.25 $ and $(x_1, y_1) = (2, 22.45)$:
\[
y - 22.45 = -5.25(x - 2)
\]
Simplify:
\[
y = -5.25x + 10.50 + 22.45
\]
\[
y = -5.25x + 32.95
\]
---
### Step 5: Answers
1. **Two points**: $(2, 22.45)$ and $(5, 6.70)$.
2. **Rate of change or slope**: $ -5.25 $, meaning the cost of each milkshake is **$5.25**.
3. **Dependent variable**: The remaining balance on the gift card ($ y $).
4. **Independent variable**: The number of milkshakes ordered ($ x $).
Let me know if you'd like further clarification!
RELATED QUESTIONS
what are the 2 points and slope for this question ? Connor uses a gift card to buy... (answered by ikleyn)

Susan has a $100 gift card to her favorite restaurant. Each day, she uses her gift card... (answered by Theo)

Write the algebraic expression that is suggested in the word statement or problem:... (answered by stanbon)

Please help me solve this question: Connor is playing a a card game called at Face Vaule. (answered by Solver92311)

Guy has a gift card that he uses to buy video games. Each game costs $7, and after buying (answered by josgarithmetic)

I need help on 5 questions on my math problems my teacher made up. Please help me solve... (answered by KMST)

Write the algebraic expresion that is suggested in the word statement or problem: (answered by solver91311)

Juan was given a gift card for a coffee shop. Each morning, Juan uses the card to buy one (answered by ikleyn)

If a friend and I each pay 50% for a $100 restaurant gift card being sold at 20% off and... (answered by stanbon)