Math

Example 2

ABC cellular phone service offers its customers a postpaid plan. Their rates of calls in a month are given in the table below. The lengths of calls in a month are expressed in minutes while the amounts are in pesos.

Length of Calls in a Month	40	80
Amount	430	710

It is known that the relationship between the amount and the length of calls in a month is linear

a.	Find a formula for the monthly bill for the phone service
b.	Determine the monthly bill when the length of calls is 75 min.

Solution

a. Since the relationship between the amount and the length of calls in a month is linear, the required formula should be in the form $y = m x + b .$ Let x be the length of calls in a month and y, the amount. To find the slope m, use the formula $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} .$ The two given ordered pairs are $(40, 430)$ and $(80, 710) .$

m = \frac{710 - 430}{80 - 40} = \frac{280}{40} = 7

Hence, $m = 7.$ To find the y-intercept b, substitute $m = 7,$ $x = 40,$ and $y = 430$ $[using$ the ordered pair $(40, 430)]$ in $y = m x + b .$ You will get:

y	=	$m x + b$	Slope-intercept form.
430	=	$7 (40) + b$	Substitute the given values.
430	=	$280 + b$	Simplify.
$430 - 280$	=	b	Subtract 280 from both sides.
150	=	b	Simplify.

Thus, the formula for the monthly bill is $y = 7 x + 150.$

b. You are given that the length of calls is 75 min, or $x = 75.$ To find y, or the amount corresponding to 75 min, substitute 75 for x in $y = 7 x + 150.$

y = 7 (75) + 150 = 675

Thus, when the length of calls is 75 min, the monthly bill is ₱675.

Applications of Linear Functions