The given table shows the number of text messages sent from a phone and the monthly cost of the phone plan.
Phone Plan Cost
Messages Sent
20
50
80
Monthly Cost ($)
41.99
44.99
47.99
To begin, we will define variables for the given quantities. Let x represent the number of text messages sent and let y represent the monthly cost. To graph the data we will plot the points as (x,y).
b
To be able to write an equation, we will first discuss whether the given data is linear. We can use the graph in Part A to show that data is linear. We will connect the points in the graph to see whether they are on the same line. Note that the number of messages sent and the monthly cost cannot be negative.
As we can see, all points lie on the same line. To write an equation for the data, we can use point-slope form.
y-y_1=m(x-x_1)
In this equation m is the slope of the line and (x_1,y_1) is a point that is on the line. We will change the parameters of the general form according to the situation stated in the problem. In this case n represents the number of the messages sent, and c represents the monthly cost.
y-y_1=m(x-x_1)
⇕
c-y_1=m(n-x_1)
From here we can use any of the given points for (x_1,y_1). To determine the slope, we can use the Slope Formula with two of the given points. Let's use (20,41.99) and (50,44.99).
We can now write the equation in point-slope form. We will substitute the slope, m= 0.1, and one of the points, say ( 20, 41.99), in the equation.
n- 41.99= 0.1(c- 20)
Finally, we will simplify the expression.
