Question

# Gopi wants to rent a tent for an outdoor celebration. The Cost of tent is Rs.500 per hour, plus an additional Rs.100 set-up fee.

a) Draw a graph to show the relationship between the number of hours the tent is rented, x, and The total cost of the tent Y.

b) What is the equation of the line in slope- intercept form?

Hint:

### First we find the total cost of the tent for every hour and make a table with x as the number of hours rented and y as the total cost of the tent. We use this data to plot a graph for the relationship.

The equation of line in slope- intercept form is y = mx + c, where m is slope and c is the y- intercept. We find m and c from the data in the table to get the required equation.

## The correct answer is: y = 500x + 100

### Step by step solution:

The cost of tent per hour = Rs.500

Set up fee = Rs.100

For the first hour, the total cost = Rs.(100 + 500) = Rs.600

In the second hour, the set up fee is still Rs.100, and the cost of tent = Rs(500*2) = Rs.1000

The total cost for 2 hours = Rs.(1000 + 100)= Rs.1100

Continuing this way,

The total cost for 3 hours = Rs.(500 × 3 + 100) = Rs.1600

The total cost for 4 hours = Rs.(500 × 4 + 100) = Rs.2100

The total cost for 4 hours = Rs.(500 × 5 + 100) = Rs.2600

Now, taking time (in hours) to be in x-axis and the total cost (in Rs.) to be y- axis, we draw the following table.

Now, we plot these points on the graph

The line intercept form of a line is y = mx + c, where is the slope of the line and is the y-intercept of the line.

First, we find the slope of the equation.

For two points and satisfying the equation, the slope is given by

Taking any two points from the table and denoting them as

, we have

m =

m = = 500

Next, for finding the y-intercept, we input any value from the table in the equation y = mx + c

We choose the first point (1,600), and using it in the above equation, we have

600 = m × 1 + c

Putting the value of m in the above relation, we have

600 = 500 × 1 + c

Simplifying, we have

600 = 500 + c

Thus, we get

c = 600 - 500 = 100

So, the y-intercept c = 100,

Using the value of m and c, we get the required equation,

y = 500x + 100

The line intercept form of a line is y = mx + c, where is the slope of the line and is the y-intercept of the line.

First, we find the slope of the equation.

For two points and satisfying the equation, the slope is given by

Taking any two points from the table and denoting them as

Next, for finding the y-intercept, we input any value from the table in the equation y = mx + c

We choose the first point (1,600), and using it in the above equation, we have

Putting the value of m in the above relation, we have

Simplifying, we have

Thus, we get

So, the y-intercept c = 100,

Using the value of m and c, we get the required equation,

Instead of using these particular points to find the slope and the y-intercept, we can use any other points from the table; we will get the same equation at the end. We can also verify this equation by inserting the points from the table and checking if the equation is satisfied. Finally, we can find the line in any other forms of a straight line.

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