SME
Grade 8 Math · Problem type
Slope and intercept in a story
Use this for “A bike rental costs $8 plus $3 an hour. What do 5 hours cost, and what do the 8 and the 3 mean?”
Chart
C = 3h + 8
Slope r = 3: up 3 for every 1 across
Intercept f = 8: it crosses the y-axis at (0, 8)
C = 3 × 5 + 8 = 23 when h = 5
This is an example. Type your own values to start a new problem.
C
=
r
×
h
+
f
Formulas
C
=
r
×
h
+
f
(amount
after
h
hours
=
change
each
hour
×
hours
+
amount
at
the
start)
23 = 3 × 5 + 8
Assumptions
•
The fee is where the line starts (the intercept); the hourly cost is its slope.
•
A negative slope means the amount goes down each step: a phone battery losing 8% an hour.
•
The intercept is the amount at 0: the cost before any hours.
Step-by-step
WE KNOW
h = 5 (hours), r = 3 (change each hour), f = 8 (amount at the start)
FIND
amount after h hours (C)
Step 1 · Find amount after h hours (C)
Use C = r × h + f (amount after h hours = change each hour × hours + amount at the start)
The change over the hours, plus the start.
C
=
3
×
5
+
8
C
=
15
+
8
C
=
23
Check
Put the numbers back in. Both sides should match.
23 = 3 × 5 + 8 ✓
Topic check
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