SME
Grade 9 Math · Problem type
A linear model in a story
Use this for “A class costs $25 to join plus $12.50 a class. What do 8 classes cost?”
Chart
y-intercept (0, 25)
C(8) = 125
More classes: 3
Added cost: $37.50
This is an example. Type your own values to start a new problem.
$
C
=
$
b
+
$
m
×
x
Δx
More classes
example
ΔC
Added cost
calculated · $
Formulas
C
=
b
+
m
×
x
125 = 25 + 12.5 × 8
ΔC
=
m
×
Δx
37.5 = 12.5 × 3
Assumptions
•
The total is the joining fee plus the rate times the count: C = b + mx.
•
b is the value when x = 0; m is how much each one more adds.
•
x is a whole number of classes, 0 or more: the domain of the story.
Step-by-step
WE KNOW
x = 8, b = $25, m = $12.50, Δx = 3
FIND
total cost (C), added cost (ΔC)
Step 1 · Find total cost (C)
Use C = b + m × x
The starting amount plus the rate for each class.
C
=
25
+
12.5
×
8
C
=
25
+
100
C
=
$125
Step 2 · Find added cost (ΔC)
Use ΔC = m × Δx
Each class more adds the rate once, whatever the starting amount.
ΔC = 12.5 × 3
ΔC = $37.50
Check
Put the numbers back in. Both sides should match.
125 = 25 + 12.5 × 8 ✓
37.5 = 12.5 × 3 ✓
← Previous lesson
Parallel and perpendicular lines
Next lesson →
Scatter plots, correlation, residuals and lines of best fit
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.