A cellular network offers two plans. Plan 1 costs R2.50 per minute. Plan 2 costs R10 plus R3 per minute. Which plan is cheaper for 20 minutes? Explain how changes in fixed fees and per-minute costs af

From previous questions:
Company 1's cost formula: $C_1 = 2.50m$
Company 2's cost formula: $C_2 = 10 + 3m$

Calculate the cost for 20 minutes for Company 1:

The cost for Company 1 for 20 minutes is R50.00.

Calculate the cost for 20 minutes for Company 2:

The cost for Company 2 for 20 minutes is R70.00.

Compare the costs:
R50.00 (Company 1) is less than R70.00 (Company 2).
Therefore, Company 1 is cheaper for 20 minutes.

A real-life example of a similar linear relationship is the cost of hiring a taxi, which often involves a fixed base fare plus a cost per kilometer traveled.

Consider the general linear equation $y = mx + c$, where $c$ is the fixed fee (y-intercept) and $m$ is the cost per minute (gradient).

• If the fixed fee increases: The graph will shift upwards parallel to its original position. The y-intercept will move higher on the y-axis.

• If the cost per minute increases: The graph will become steeper. The gradient of the line will increase, causing it to rotate upwards around the y-intercept.