⚠️ Top Mistakes on Word Problems
- Not labelling what m and b mean: Always state "slope = ___ means ___" and "y-intercept = ___ means ___".
- Wrong sign for decreasing quantities: If something is draining, spending, or cooling — slope is NEGATIVE.
- Intercept interpretation: x-intercept = when y is zero (quantity runs out). y-intercept = starting amount (when x=0).
- Units matter: "$45 per hour" means m=45 with units dollars/hour. Always include units in your interpretation.
Q1 Easy
Cat fountain: 200 mL, drains 25 mL/hour
1
Slope = −25 (draining → negative). Starting value = 200 → b=200
2
Equation: W = −25h + 200
3
After 3 hours: W = −25(3)+200 = −75+200 = 125 mL
W = −25h + 200 | After 3 hrs: 125 mL
Q2 Easy
Savings: $60 start, $15/week
1
m=15 (saving = positive), b=60
2
S = 15w + 60
3
After 8 weeks: S = 15(8)+60 = 120+60 = $180
S = 15w + 60 | After 8 weeks: $180
Q3 Easy
Baking website: $35 membership + $0.05/gram
1
m=0.05, b=35. Equation: C = 0.05g + 35
2
400 grams: C = 0.05(400)+35 = 20+35 = $55
C = 0.05g + 35 | 400g order = $55
Q4 Medium
Balloon rising: 2.5 ft/sec from ground
1
m=2.5, b=0. Equation: H = 2.5s
2
After 12 sec: H = 2.5(12) = 30 feet
3
When H=50: 50 = 2.5s → s = 20 seconds
H = 2.5s | 12s = 30 ft | 50 ft at s=20 seconds
Q5 Medium
Cat shelter: $40 fee + $2/day boarding
1
m=2, b=40. Equation: C = 2d + 40
2
7 days: C = 2(7)+40 = 14+40 = $54
3
C=64: 64 = 2d+40 → 2d=24 → d=12 days
C = 2d + 40 | 7 days = $54 | $64 = 12 days
Q6 Medium
Rin's fund: $450, spends $30/week
1
m=−30, b=450. Equation: A = −30w + 450
2
x-intercept (A=0): 0=−30w+450 → w=15 weeks. Meaning: the fund runs out after 15 weeks.
3
y-intercept (w=0): A=450. Meaning: Rin starts with $450 in the fund.
A = −30w + 450 | x-int (15,0): fund runs out at week 15 | y-int (0,450): starting amount
Q7 Medium
Concert: student $6, adult $9, total $540
1
Standard form: 6s + 9a = 540 (or simplified: 2s + 3a = 180)
2
x-int (a=0): 6s=540 → s=90 → (90,0). Meaning: 90 student tickets sold if no adults attended.
3
y-int (s=0): 9a=540 → a=60 → (0,60). Meaning: 60 adult tickets sold if no students attended.
6s + 9a = 540 | (90,0): 90 students only | (0,60): 60 adults only
Q8 Hard
Temperature: 48°F at 7AM, rises 4°F/hour
1
m=4, b=48. Equation: T = 4h + 48 (h = hours after 7 AM)
2
Noon = 5 hours after 7 AM (h=5): T = 4(5)+48 = 20+48 = 68°F
3
When T=72: 72=4h+48 → 4h=24 → h=6. 7 AM + 6 hours = 1:00 PM
4
5 AM is 2 hours BEFORE 7 AM → h=−2: T=4(−2)+48=−8+48=40°F
T = 4h + 48 | Noon: 68°F | 72°F at 1 PM | 5 AM: 40°F
Q9 Hard
Cat fountain: 25,000 mL, drains 500 mL/hour
1
m=−500, b=25000. Equation: W = −500h + 25000
2
Half empty = 12,500 mL: 12500=−500h+25000 → 500h=12500 → h=25 hours
3
x-intercept (W=0): 0=−500h+25000 → h=50 hours. Meaning: fountain empties after 50 hours.
4
y-intercept (h=0): W=25,000 mL. Meaning: the fountain starts full at 25,000 mL.
W = −500h + 25000 | Half empty at h=25 hrs | Empty at h=50 hrs | Starts at 25,000 mL
Q10 Hard
Balloon kits: Kit A = $25 + $0.30/balloon; Kit B = $40 + $0.15/balloon
1
Kit A: C = 0.30n + 25 Kit B: C = 0.15n + 40
2
Set equal: 0.30n + 25 = 0.15n + 40
3
Subtract 0.15n: 0.15n + 25 = 40 → 0.15n = 15 → n = 100 balloons
4
At 150 balloons: A = 0.30(150)+25 = 45+25 = $70 B = 0.15(150)+40 = 22.50+40 = $62.50
5
Kit B is cheaper at 150 balloons ($62.50 vs $70).
Kit A: C=0.30n+25 | Kit B: C=0.15n+40 | Same cost at 100 balloons | Kit B cheaper at 150
🤖 AI Prompts for Word Problems
If you don't know how to start a word problem:"I have an Algebra 1 word problem about a linear situation. Can you teach me a strategy for identifying the slope (rate), y-intercept (starting value), and the variable (what changes) from a word problem description?"
If you struggle interpreting x and y intercepts:"In a real-world linear equation problem, how do I explain what the x-intercept and y-intercept mean in context? Can you give me two examples — one where y decreases and one where y increases?"
For Q10 type (two equations, find when they're equal):"How do I find when two linear equations have the same value? Walk me through setting them equal and solving algebraically. This is called a 'break-even point'."
📺 Learn More
- Khan Academy: Search "linear equations word problems" under Algebra 1
- YouTube: Search "slope intercept form word problems Algebra 1"
- Khan Academy: Search "interpreting intercepts of linear functions"
- YouTube: Search "standard form word problems Algebra 1 intercepts"
🎉 Congratulations, Alishba!
You have completed all 60 questions across 6 topics of Algebra 1 Linear Equations.
You've practised slope, slope-intercept form, standard form, intercepts, writing equations, and word problems.
You are well prepared for your Frisco ISD exams. Keep going — you've got this! 🐱🎵🎈🍰