Question

1. suppose a 5-minute overseas call costs $6.95 and a 10-minute call costs $11.80. write and solve a linear equation to find the cost for making an 18-minute call.

Explanation:

Step1: Define linear cost model

Let $x$ = call minutes, $y$ = total cost. Model: $y = mx + b$, where $m$ = rate, $b$ = fixed fee.

Step2: Plug in given points

For $(5, 6.95)$: $6.95 = 5m + b$
For $(10, 11.80)$: $11.80 = 10m + b$

Step3: Solve for $m$

Subtract first equation from second:
$$11.80 - 6.95 = (10m + b) - (5m + b)$$
$$4.85 = 5m$$
$$m = \frac{4.85}{5} = 0.97$$

Step4: Solve for $b$

Substitute $m=0.97$ into $6.95 = 5m + b$:
$$6.95 = 5(0.97) + b$$
$$6.95 = 4.85 + b$$
$$b = 6.95 - 4.85 = 2.10$$

Step5: Final cost equation

The linear equation is $y = 0.97x + 2.10$

Step6: Calculate 18-minute cost

Substitute $x=18$:
$$y = 0.97(18) + 2.10$$
$$y = 17.46 + 2.10 = 19.56$$

Answer:

The linear equation is $y = 0.97x + 2.10$, and the cost of an 18-minute call is $\$19.56$