Quiz Answers and Explanations

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📚 Part 1: Multiple Choice — Answers & Explanations

1. Which equation has slope 3 and y-intercept -2?

y = 3x - 2 (Answer)

y = -3x - 2

y = 3x + 2

y = -3x + 2

Explanation: Slope m = 3 and y-intercept b = -2 plug into y = mx + b to get y = 3x - 2.

2. From the table: (1, 3), (2, 5), (3, 7). Which function models this relationship?

y = 2x + 1 (Answer)

y = x + 2

y = 3x - 0

y = 2x - 1

Explanation: Slope = change in y / change in x = (5-3)/(2-1)=2. Use point (1,3): 3 = 2(1)+b → b = 1. So y = 2x + 1.

3. A taxi charges a $2 base fare plus $1.50 per mile. Which is the correct cost function C(m)?

C(m) = 1.50m + 2 (Answer)

C(m) = 2m + 1.50

C(m) = 1.50(m + 2)

C(m) = 2 + 1.50

Explanation: Rate per mile is slope 1.50 (multiply by m). Base fare is y-intercept 2, so C(m)=1.50m+2.

4. Check all statements that are true about linear functions:

Slope is the constant rate of change. (True)

The y-intercept is the value when x = 0. (True)

All linear functions must pass through the origin. (False)

The graph of a linear function is a straight line. (True)

Explanation: Only lines with b = 0 pass through the origin; otherwise the intercept is b ≠ 0.

✏️ Part 2: Short Answers — Work & Explanations

5. Write the linear equation that passes through (2, 4) and (5, 10). Show your work.

Step 1: Find slope m = (10 - 4) / (5 - 2) = 6 / 3 = 2.
Step 2: Use point-slope with (2,4): y - 4 = 2(x - 2).
Step 3: Convert to slope-intercept: y - 4 = 2x - 4 → y = 2x.
Final answer: y = 2x.
Note: Line passes through (0,0) because b = 0.

6. A phone's value drops from $800 to $560 in 4 months. Write V(t) = mt + b to model value over months t. Show work and write the function.

Step 1: Slope m = (560 - 800) / (4 - 0) = -240 / 4 = -60 dollars per month.
Step 2: At t = 0, value b = 800.
Final function: V(t) = -60t + 800.
Interpretation: Phone loses $60 each month.

7. For y = -1.5x + 12, find the x-value when y = 0. Show steps and answer.

Set 0 = -1.5x + 12.
Solve: -1.5x = -12 → x = (-12) / (-1.5) = 8.
Final answer: x = 8.

8. A plant is 5 inches tall and grows 3 inches every 2 weeks. Let t be weeks. Write a linear function h(t) and explain what the slope means in one sentence.

Growth rate per week = 3 inches / 2 weeks = 1.5 inches per week.
Initial height b = 5 inches.
Function: h(t) = 1.5t + 5.
Interpretation: The slope 1.5 means the plant grows 1.5 inches each week.

🔬 Part 3: Extension & Reflection — Answers

9. Extension challenge: Are these the same line? 2x - 4y = 8 and y = 0.5x - 2

Yes (Answer)

Explanation: Rearrange 2x - 4y = 8 → -4y = -2x + 8 → y = (1/2)x - 2, which matches y = 0.5x - 2. They are the same line.

10. Self-check: Tick the boxes that describe your readiness.

I can find slope from two points.

I can write an equation in y = mx + b form.

I can interpret slope and intercept in context.

Teacher notes & supports: I can... write linear functions from tables, graphs, and word problems. Success criteria: identify slope & intercept, write y = mx + b, interpret slope as rate of change. Differentiation: provide worked examples, allow calculator, offer graphing tool. Extension: convert between forms and compare lines. Dyslexia-friendly: read aloud, use larger font and extra spacing.