The flag-down fare of a taxi is PKR m. The taxi charges PKR n for each kilometer it travels. Use the graph to find the value of m and of n.
Understand the Problem
The question describes a taxi fare system with a flag-down fare (m) and a per-kilometer charge (n). It asks to find the values of 'm' and 'n' using the provided graph which plots charges (PKR) against distance travelled (km). To solve this, we need to read the y-intercept and slope of the line plotted, the y intercept is the flag down fare representing 'm', and the slope of the line will represent 'n'.
Answer
$m = 200$ $n = 100$
Answer for screen readers
$m = 200$ $n = 100$
Steps to Solve
- Determine the flag-down fare 'm'
The flag-down fare is the charge when the distance travelled is zero. This is the y-intercept of the graph. From the graph, the y-intercept is 200 PKR. Therefore, $m = 200$.
- Determine the charge per kilometer 'n'
The charge per kilometer is represented by the slope of the line. We can calculate the slope using two points on the line. From the graph, we can read the points $(0, 200)$ and $(2, 400)$.
- Calculate the slope
The slope $n$ is calculated as the change in charge divided by the change in distance: $$ n = \frac{y_2 - y_1}{x_2 - x_1} $$
Substitute the identified points $(0, 200)$ and $(2, 400)$ into the equation: $$ n = \frac{400 - 200}{2 - 0} = \frac{200}{2} = 100 $$
Thus $n = 100$.
$m = 200$ $n = 100$
More Information
The flag-down fare is 200 PKR, and the taxi charges 100 PKR for each kilometer travelled.
Tips
A common mistake is misreading the graph and not accurately identifying the points for calculating the slope. Another mistake is mixing up the x and y values when calculating the slope, leading to an incorrect result. Also, students may confuse the y-intercept with the x-intercept. To avoid these mistakes, carefully read the values from the graph and double-check the slope calculation.
AI-generated content may contain errors. Please verify critical information
