RATIOS & PROPORTIONAL RELATIONSHIPS
A ratio compares what two quantities?
Two different quantities
What is y = kx called?
Proportional relationship
-8 + 12 = ?
4
What does ≤ mean?
Less than or equal to
If 1 ticket costs $8, what is the cost of 5 tickets?
$40
Write the ratio 6 boys to 9 girls in simplest form.
2:3
If k = 6, write the equation.
y = 6x
-15 + (-6) = ?
-21
Solve: x - 4 > 9
x > 13
A car travels 60 miles in 1 hour. How far in 3.5 hours?
210 miles
Is the table proportional?
x: 2, 4, 6
y: 6, 12, 18
Yes
Find k if y = 45 and x = 9.
k = 5
-6 × 9 = ?
-54
Solve: -5x ≤ 20
x ≥ -4
A worker earns $120 in 15 hours. What is hourly rate?
$8 per hour
Which situation is proportional? Explain your reasoning:
A) 2 notebooks for $5, 4 notebooks for $10
B) 2 notebooks for $5, 4 notebooks for $9
A only — same unit rate
A graph passes through (2, 10). Is the relationship proportional? Explain.
No, For a relationship to be proportional, it must:
✔ Pass through the origin (0, 0)
✔ Have a constant ratio (k)
Solve: -3 + 4 × (-2)
-11
A student solves -2x > 8 and gets x > 4. What mistake did they make?
Forgot to flip inequality sign
Two phones:
Plan A = $30 + $0.10 per text
Plan B = $50 flat fee
At what number of texts is Plan B better?
More than 200 texts
A car travels 150 miles in 2.5 hours. A second car travels 240 miles in 4 hours. Which is faster? Show reasoning.
Both = 60 mph, same speed
A student earns $84 for 12 hours of work. Write an equation and determine how much they earn in 18 hours.
k = 7, y = 7x, $126
A submarine is at -120 feet. It rises 35 feet, then drops 18 feet. What is its final position?
-103 feet
A number increased by 6 is less than 3 times the number. Write and solve the inequality.
x + 6 < 3x → x > 3
A machine produces 18 items in 6 minutes. At this rate, how many items in 45 minutes? Explain method.
135 items