The taxi fare in a city is such that rs.50 is the fixed amount for the first two kilometers and rs.10 for the subsequent kilometers is charged.Taking the distance covered as " x"km and total fare as rs ." Y" ,write a linear equation in "x" and "y" .Represent it graphically
To write a linear equation in terms of x and y for the taxi fare, we need to consider the fixed amount for the first two kilometers and the subsequent charge for the remaining distance.
The fixed amount for the first two kilometers is Rs. 50. So, if the distance covered is less than or equal to 2 km, the total fare would be Rs. 50.
If the distance covered is more than 2 km, an additional charge of Rs. 10 per kilometer is applied.
Here's the equation for the taxi fare:
If x ≤ 2, then y = 50
If x > 2, then y = 50 + 10(x-2)
Graphically, we can represent this equation as follows:
1. Plot the point (2, 50) on the graph. This represents the first two kilometers with a fixed fare of Rs. 50.
2. Draw a straight line passing through the point (2, 50) with a slope of 10. This represents the subsequent charge of Rs. 10 per kilometer after the first two kilometers.
Note: The fare will increase linearly as the distance covered increases.
Thus, this graph will represent the linear equation for the taxi fare in terms of x and y.
To write a linear equation representing the taxi fare, we need to consider the two cases: the fixed fare for the first two kilometers and the subsequent fare for the remaining kilometers.
Case 1: Fixed fare for the first two kilometers
The fixed fare for the first two kilometers is ₹50. Let's assume this part of the fare as F1.
Case 2: Fare for the remaining kilometers
The fare for the remaining kilometers is ₹10 per kilometer. Let's assume the distance covered after the first two kilometers as x-2, where x is the total distance covered. The fare for this part would be 10 * (x-2), which can be written as F2 = 10(x-2).
Total Fare:
The total fare, Y, is the sum of F1 and F2. Therefore, the linear equation representing the taxi fare is:
Y = F1 + F2
Y = 50 + 10(x-2)
Y = 50 + 10x - 20
Y = 10x + 30
Now, let's represent this equation graphically.
To create a graph, we'll use the x-axis to represent the distance covered (x) and the y-axis to represent the total fare (Y).
Plotting the graph:
1. Choose an appropriate scale for the x and y-axis.
2. Plot the y-intercept, which is 30 on the y-axis.
3. Determine the slope of the line, which is 10. Since it's positive, the line will be upward sloping.
4. Use the slope to find additional points on the line. For example, if x = 0, Y = 30. If x = 5, Y = 80.
5. Join the points to form a straight line.
The graph will show the relationship between the distance covered (x) and the total fare (Y).
sorry. that's ⌈x-2⌉
y =
0.50 for x <= 2
0.50 + 0.10(x-2) for x > 2
technically, it is a step function, so
y = 0.50 + 0.10⌈x-1⌉ for x > 2