Thus, y = 20x + 150 represents the linear relationship between y, the bill amount in Rupees, and x, the number of GB of the internet data used.
Can you guess what the numbers 20 and 150 in the equation y = 20x + 150 represent?
Step-by-step solution
Idea: The company charges a fixed monthly fee plus a cost per GB. The number multiplied by x changes with the data used; the number on its own does not.
- Each extra GB adds 20 to the bill (for example 10 GB → ₹350, 11 GB → ₹370). So 20 is the cost per GB: ₹20 per GB.1 mark
- If no data is used, x = 0 and y = 150. So 150 is the fixed monthly fee: ₹150.1 mark
Check: Bill for 20 GB = 20 × 20 + 150 = 400 + 150 = 550 ✓, as observed.
Answer to write in the exam
y = 20x + 150
Increase of 1 GB increases y by ₹20 ⇒ 20 = cost per GB (₹)
x = 0 ⇒ y = 150 ⇒ 150 = fixed monthly fee (₹)
∴ 20 is the cost per GB and 150 is the fixed monthly fee
Common mistakes that cost marks
- Saying 150 is the bill for 1 GB. For 1 GB the bill is 20 + 150 = ₹170.
- Swapping the meanings: calling 150 the cost per GB.
- Saying 20 is the number of GB used. x is the data used; 20 is the rate.
How this can come in the exam
A taxi fare is y = 14x + 40 for x km. The number 40 represents
- the fare per km
- the fixed starting charge
- the distance travelled
- the total fare for 1 km
Show answer
(B) the fixed starting charge
At x = 0 the fare is 40, so it is the fixed charge.
A tutor’s monthly bill is y = 450x + 1000 for x classes. Interpret 450 and 1000, and find the bill for 8 classes.
Show answer
450 = fee per class; 1000 = fixed monthly charge (1 mark). Bill = 3600 + 1000 = ₹4600 (1 mark).Try one yourself
A water bill is y = 8x + 120 for x kilolitres. What do 8 and 120 mean? Find the bill for 25 kilolitres.
Show answer
8 = ₹8 per kilolitre; 120 = fixed charge. Bill = 200 + 120 = ₹320.
More questions like this
- 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.
- A gym charges a fixed monthly fee and an additional cost per hour for using the badminton court. A student using the gym observed that when she used the badminton court for 10 hours, her bill was ₹800. When she used it for 15 hours, her bill was ₹1100. If the monthly bill y depends on the hours of the use of the badminton court, x, according to the relation y = ax + b, find the values of a and b.
- Consider the relationship between temperature measured in degrees Celsius (°C) and degrees Fahrenheit (°F), which is given by °C = a °F + b. Find a and b, given that ice melts at 0 degrees Celsius and 32 degrees Fahrenheit, and water boils at 100 degrees Celsius and 212 degrees Fahrenheit.
(Hint: When °C = 0, °F = 32 and when °C = 100, °F = 212. Use this information to find a and b, and thus, the linear relationship between °C and °F.) - Identify other points on the line by completing the following table.
x: 1, 2, 5, 7, 9, 12, 20
y: 3, __, __, 15, __, __, __ - Let us plot the points (−1, −3), (0, 0), (1, 3), (3, 9), (4, 12) in the coordinate plane on a graph paper as shown in the figure. Join the points (−1, −3) and (4, 12) using a ruler. Doing so, observe that all five points lie on a straight line. Can you guess the equation of this line by looking at the relationship between the x and y coordinates of each point?