Maths-

General

Easy

Question

# The graph shows the subscription cost to a certain club in town. Write an equation of the Application

line. Explain what the slope and y-intercept mean in this situation. Then find the total

cost for 2 years.

Hint:

### 1. When we have 2 points that lie on a given line then we can find the equation of the said line by using the 2-point formula-

(y-y1) = (y2-y1) × (x-x1)

(x2-x1)

2. The slope of a line can be defined as the change in y coordinates of any 2 points on that line corresponding to the change in the x coordinates of those 2 points. This is generally referred to as the rise to run ratio of the given line i.e. how much did the y-coordinates rise vis-a-vis how long a distance was covered by the x-coordinates.

3. y-intercept for any line refers to the point at which the given line intersects with the Y-axis. At this point the x-coordinate is 0.

## The correct answer is: The given line can be written as- y = 100/3 x + 100. Its slope (i.e. change in cost for a given change in time period) is 100/3 or 33.33. Its Y-intercept (i.e. cost at 0 months or before starting operations) is $100. Also, cost of functioning for 2 years = $900.

### step-by-step solution:-

From the given graph, we can observe that-

monthly cost of subscription in Dollars has been given and a line representing such cost has been plotted on the graph.

We observe that the given line passes through 2 points (0,100) & (6,300).

Hence, x1 = 0, y1 = 100, x2 = 6 & y2 = 300.

Coordinates of any point that lie on a line, when substituted in the equation of the given line, satisfies the equation.

Hence, we can find out the equation of the given lie using 2 point formula-

(y-y1) = (y2-y1) × (x-x1)

(x2-x1)

∴ (y-100) = (300 -100) × (x-0)

(6-0)

∴ (y-100) = 200 × x

6

∴ 6 × (y-100) = 200x ................................................................................. (Multiplying both sides by 6)

∴ 6y - 600 = 200x

∴ 6y = 200x + 600

∴ y = 200/6 x + 600/6 ............................................................... (Dividing both sides by 6)

∴ y = 100/3 x + 100 ..................................................................... (Equation i)

Comparing Equation i with the slope intercept form of a line i.e. y = mx + b, we get-

Slope = m = 100/3

& Y-intercept = b = 100

the months that it is functioning.

since the slope = 100/3 ≈ 33.33, we can say that for every month that the club functions (From the first month), its subscription cost increases by $33.33.

Also, y-intercept for any line refers to the point at which the given line intersects with the Y-axis.

At this point the x-coordinate is 0.

This means that when the value of x-coordinate is 0, the value of y-coordinate is $100.

For the given situation, this means that the club has to incur a subscription cost of $100, irrespective of whether it functions for its customers or not. i.e. even before starting its operations for earning revenue, it has to incur $100 towards subscription cost.

Now, Since the given equatuion is represented in terms of months, to find the total cost for 2 years, we first need to convert this time period (2 years) into months. i.e. 2 ×12 months = 24 months.

∴ We need to find the total subscription cost to the club for 24 months.

∴ We substitute x = 24 in Equation i, to find the total cost = y

∴ y = 100/3 x + 100

∴ y = 100/3 × 24 + 100

∴ y = 100 × 8 + 100

∴ y = 800 + 100

∴ y = 900.

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