Back to Ganita Manjari: Class 9 Mathematics (NCE...BackConcept

Finding Linear Relationships

Formulate a linear relationship y = ax + b from given conditions.

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The Form y = ax + b

Introduce finding relationships using y = ax + b.

A linear relationship between two variables $x$ and $y$ can often be expressed as the equation $y = ax + b$ . In this equation, $a$ and $b$ are constants that determine the specific rule connecting the variables.

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If you have two pairs of

(x, y)

values, you can substitute them into

y = a x + b

to create two separate equations. This gives you a system of linear equations that allows you to solve for the constants

a

and

b

Telecom Bill Calculation

Worked example solving for a and b.

Problem. A telecom company charges a fixed monthly fee and an additional cost per GB of internet data used. A student observes that when she used 10 GB, her bill was ₹350. When she used 20 GB, her bill was ₹550. If the monthly bill $y$ depends on the amount of data used, $x$ (in GB), according to the relation $y = ax + b$ , find the values of $a$ and $b$ .

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Gym Charges

Faded example based on Exercise 2.5 Q2.

0 of 3 blanks filled

Let's formulate the linear relationship $y = ax + b$ for the gym charges, where $b$ is the fixed monthly fee and $a$ is the hourly cost. For 10 hours of use, the bill is ₹800, giving the equation: $800 =$ $a + b$ .

For 15 hours, the bill is ₹1100, which gives the equation: $1100 = 15a + b$ . From the first equation, we can express the fixed fee as $b = 800 - 10a$ .

Substituting this expression into the second equation yields: $1100 = 15a + (800 - 10a)$ , which simplifies to $300 =$ $a$ .

Solving this gives the hourly rate $a =$ , and substituting back gives the fixed fee $b = 200$ .

Order the Solving Steps

Order the steps to find a and b.

Drag the steps into the correct logical order for solving simultaneous linear equations to find constants 'a' and 'b'.

Drag to reorder

Temperature Conversion

Guided problem based on Exercise 2.5 Q3.

Consider the relationship between temperature in degrees Celsius (°C) and Fahrenheit (°F) given by

C = aF + b

. Given that ice melts at

0^\circ C

and

32^\circ F

, and water boils at

100^\circ C

and

212^\circ F

, solve for the constants

a

and

b

step-by-step.

Identify the given (F, C) pairs

List the two pairs of coordinate values provided in the problem.

Write the two equations

Substitute the given pairs into C = aF + b.

Isolate 'b' in the first equation

Rearrange your simpler equation to express b in terms of a.

Substitute and solve for 'a'

Substitute your expression for b into the second equation and solve for a.

Solve for 'b' and state the final values

Calculate b using the value of a, then state both constants.

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