Linear Relationships
• Class 9 Mathematics • Ganita Manjari
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Question 1
A learning platform charges a fixed monthly fee
and an additional cost for each digital learning
module accessed.
When a student accesses
10 modules, her bill is
₹400.
When she accesses
14 modules, her bill is
₹500.
If the monthly bill is represented by
y = ax + b
where x is the number of modules,
find the values of a and b.
हिंदी में समझें:
हमारे पास दो situations हैं:
10 modules → ₹400
14 modules → ₹500
Formula है:
y = ax + b
दोनों values को formula में डालकर
दो equations बनाएँगे।
फिर दोनों equations को subtract करके
पहले a निकालेंगे और उसके बाद
b निकालेंगे।
Step-by-Step Solution:
Given:
y = ax + b
First observation:
x = 10, y = 400
400 = 10a + b
Second observation:
x = 14, y = 500
500 = 14a + b
Subtract the first equation from the second:
500 − 400 = 14a − 10a
100 = 4a
a = 25
अब पहली equation में a = 25 रखें:
400 = 10(25) + b
400 = 250 + b
b = 150
इसलिए:
y = 25x + 150
✅ Answer:
a = 25
b = 150
Linear relationship:
y = 25x + 150
Question 2
A gym charges a fixed monthly fee and an additional
amount per hour for using its badminton court.
For 10 hours of badminton-court use,
the bill is ₹800.
For 15 hours of use,
the bill is ₹1100.
If the monthly bill y depends on the number of hours x
according to
y = ax + b
find a and b.