WARM-UP — 5 MINUTES

Quick Review — Slope & Y-Intercept

What do you remember from yesterday? Show me with hand signals!

👍 I remember! 🤚 Kinda... 👎 Need help

Table A — Find the slope

xy
14
28

Use Desmos: + → table → Add regression

slope (m) = ___

Table B — Find slope AND y-intercept

xy
03
29

Use Desmos: + → table → Add regression

slope (m) = ___   y-int (b) = ___

Remember: m = MULTIPLIER (touching x)  |  b = BONUS (by itself)

I DO — WRITING y = mx + b

Working at La Pulga (Flea Market) 🛍️

🛍️ LA PULGA 🛍️
Dallas Flea Market
HELP WANTED
$10/hr + $20 setup
👕 👖 👟 🧢 👜
You earn money for each hour you work PLUS a bonus for setting up!

Building the Equation

What changes? You earn $10 for each hour → that's the slope (m) = 10
What stays the same? You always get $20 for setup → that's the y-intercept (b) = 20
y = 10x + 20
m = MULTIPLIER ($10 per hour)  |  b = BONUS ($20 setup)
🖩 Verify with Desmos! Enter (0, 20) and (1, 30) into table → Add regression → Confirms: y = 10x + 20 ✅
I DO — SOLVING EQUATIONS WITH DESMOS

When Are Two Plans EQUAL? 📱

The Scenario

Two phone plans:

Plan A: 15x + 30 (per month)
Plan B: 10x + 55 (per month)

When do they cost the SAME?

🖩 Desmos Steps

15a + 30 ~ 10a + 55
Desmos shows: a = 5

Both plans cost the same at 5 months!

⚠️ NO "x"!

You CANNOT use the letter "x" when solving with tilde!

Desmos treats x as a graphing variable.

Change x to "a" (or any other letter)!

❌ 15x + 30 ~ 10x + 55 → Won't work!

✅ 15a + 30 ~ 10a + 55 → a = 5!

3 Steps:
  1. Change every x to "a"
  2. Type the WHOLE thing with ~ (tilde)
  3. Read the answer!
WE DO — GUIDED PRACTICE

Writing Equations: State Fair of Texas 🎡

🎡 "At the State Fair, admission costs $18 and each ride costs $4."

What's the equation for total cost (y) after x rides?

What changes per ride? $4 per ride → m (slope) = 4 ✅
What's the starting cost? $18 admission → b (y-intercept) = 18 ✅
Write the equation: y = ____x + ____
Verify with Desmos: Enter (0, ____) and (1, ____) → + → table → Add regression → Does Desmos confirm? ____
Think: After 5 rides, the total cost = 4(5) + 18 = $____
📋 Writing y = mx + b
☐ What CHANGES? → m
☐ What STARTS at? → b
☐ Write: y = mx + b
☐ Verify with Desmos!
🧠 Remember:
m = MULTIPLIER (per each)
b = BONUS (starting value)
WE DO — GUIDED PRACTICE

Solving: When Does Plan A = Plan B? 📱

📱 Plan A: 4x + 8   |   Plan B: 2x + 20   →   When are they equal?
Step 1: Change x to "a" → 4a + 8 = 2a + 20 ✅
Step 2: Type with tilde: 4a + 8 ~ 2a + 20 ✅
Step 3: Desmos shows: a = ____ → so x = ____
Step 4 — Check:
Left side: 4(__) + 8 = ____
Right side: 2(__) + 20 = ____
Equal? ____
⚠️ Solving Checklist
☐ Change x → "a"
☐ Use ~ not =
☐ Read the answer
☐ CHECK both sides!
Example:
3a + 56 ~ 17a
→ Desmos: a = 4
→ Answer: x = 4

📌 Day 2 Reference Cheat Sheets

Verbal to Desmos Checklist

Verbal to Desmos

Finding the Equation

Finding the Equation

🎫 Exit Ticket — Day 2

1. At the State Fair of Texas, admission costs $18 and each ride costs $4. Which equation represents the total cost (y) for x rides?

A. y = 18x + 4
B. y = 4x + 18
C. y = 22x
D. y = 4x − 18

2. Solve: 3x + 12 = x + 28

(Hint: change x to another letter in Desmos, use ~)

A. x = 4
B. x = 8
C. x = 16
D. x = 20

Remember: Change x → "a", use ~ not =, read Desmos answer!

1 / 7