Can you guess what the numbers 20 and 150 in the equation y = 20x + 150 represent? Class 9

Can you guess what the numbers 20 and 150 in the equation y = 20x + 150 represent? Class 9

Question 1.

Can you guess what the numbers 20 and 150 in the equation y = 20x + 150 represent? Class 9

Answer:

In the equation y = 20x + 150,

a = 20 represents the cost per GB of internet data used.

b = 150 represents the fixed monthly fee charged by the company.

Question 2.

A learning platform charges a fixed monthly fee and an additional cost per digital learning module accessed. A student observes that when she accessed 10 modules, her bill was ₹ 400. When she accessed 14 modules, her bill was ₹500. If the monthly bill y depends on the number of modules accessed, x, according to the relation y = ax + b, find the values of a and b. Class 9

Solution:

Number of modules accessed = x

Total monthly bill = y

According to the given conditions,

When x = 10, y = 400, and

When x = 14, y = 500

Substituting the values of x and y in

y = ax + b, we get

400 = 10a + b ...(i)

500 = 14a + b ...(ii)

From (i),

b = 400 - 10a ...(iii)

Substituting b = 400 - 10a in equation (ii), we get

500 = 14a + (400 - 10a)

∴ 500 = 4a + 400

∴ 4a = 500 - 400

∴ 4a = 100

∴ a = $\frac{100}{4}$ = 25

Substituting a = 25 in (iii), we get

b = 400 - 10(25) = 400 - 250

∴ b = 150

∴ The value of a is ₹25, and the value of b is ₹150.