To solve these problems, we need to write equations in slope-intercept form. The slope-intercept form of a line is:
y = mx + b
Where:
-
m is the slope (rate of change)
-
b is the y-intercept (starting value when x = 0)
We’ll go problem by problem and identify what changes (slope) and what starts at a fixed value (intercept).
---
Problem 1: You rent a bicycle for $20 plus $2 per hour.
- Starting cost (when you rent it, even if 0 hours): $20 → this is
b
- Cost increases by $2 each hour → this is
m
- Let’s say
x = number of hours,
y = total cost
Equation:
y = 2x + 20
✔ Check: If x=0, y=20 ✔️; if x=1, y=22 ✔️
---
Problem 2: An auto repair shop charges $50 plus $25 per hour.
- Starting fee: $50 →
b
- Hourly rate: $25 →
m
- x = hours, y = total cost
Equation:
y = 25x + 50
✔ Check: x=0 → y=50; x=2 → y=100 ✔️
---
Problem 3: A candle is 6 inches tall and burns at a rate of ½ inch per hour.
- Starts at 6 inches →
b = 6
- Burns down → decreasing, so slope is negative:
-½
- x = hours, y = height remaining
Equation:
y = -½x + 6
✔ Check: x=0 → y=6; x=2 → y=5 ✔️
---
Problem 4: The temperature is 15° and is expected to fall 2° each hour during the night.
- Starts at 15° →
b = 15
- Falls 2° per hour → slope =
-2
- x = hours, y = temperature
Equation:
y = -2x + 15
✔ Check: x=0 → y=15; x=3 → y=9 ✔️
---
Problem 5: A computer technician charges $75 for a consultation plus $35 per hour.
- Base charge: $75 →
b
- Per hour: $35 →
m
- x = hours, y = total cost
Equation:
y = 35x + 75
✔ Check: x=0 → y=75; x=1 → y=110 ✔️
---
Problem 6: The population of Pine Bluff is 6791 and is decreasing at the rate of 7 per year.
- Starting population: 6791 →
b
- Decreasing by 7 per year → slope =
-7
- x = years, y = population
Equation:
y = -7x + 6791
✔ Check: x=0 → y=6791; x=1 → y=6784 ✔️
---
Final Answer:
1. y = 2x + 20
2. y = 25x + 50
3. y = -½x + 6
4. y = -2x + 15
5. y = 35x + 75
6. y = -7x + 6791
Parent Tip: Review the logic above to help your child master the concept of writing equations practice worksheet.
