melanie and patrick have different phone services. the relationship of the monthly cost, y dollars, to send or receive x text messages, is a linear function. the cost of patricks texting is described by y = 0.03x + 5. the cost of melanies texting is shown in the table

Let's find out Melanie's monthly texting cost function using the table. We are given multiple points that the line describing her monthly text costs passes through, so we can use the slope formula to calculate the slope of this line first.

m = (y2 - y1) / (x2 - x1)

Substitute (5, 1.25) and (10, 2.50) into this formula.

m = (2.5 - 1.25) / (10 - 5)
m = 1.25 / 5
m = 0.25

Now we can use the point-slope equation to determine the line that describes Melanie's monthly texting cost.

I'm going to use the point (5, 1.25) and the slope m = 0.25.

y - y1 = m(x - x1)
y - 1.25 = 0.25(x - 5)
y - 1.25 = 0.25x - 1.25
y = 0.25x

We have Melanie's function:

y = 0.25x

We have Patrick's function:

y = 0.03x + 5

We want to determine which service is cheaper when 50 texts are sent/received in one month.

The number of texts sent and received is represented with the variable "x", and the cost of this service is represented with the variable "y".

All we need to do is substitute 50 for x in both equations to see if Melanie or Patrick's service is cheaper.

Starting with Melanie:

y = 0.25x
y = 0.25(50)
y = 12.50

Now with Patrick:

y = 0.03x + 5
y = 0.03(50) + 5
y = 1.5 + 5
y = 6.5

Patrick's service is substantially cheaper than Melanie's service when 50 texts are sent or received in one month.