Question

Application problem with a linear function: Finding a coordinate given two points

Answer 1

The monthly cost for 81 minutes is $19.47

Using the information given , we can determine the linear equation for the graph.

The slope-intercept form of the equation is expressed as ;

• y = bx + c ; b = slope , c = intercept

Using the pair of points; (54, 17.04) ; (86, 19.92)

The slope = (19.92 - 17.04) / (86 - 54)

slope, b = 0.09

Now we can calculate c ;

17.04 = 0.09(54) + c

17.04 = 4.86 + c

c = 12.18

The linear equation would be ;

• y = 0.09x + 12.18

B.)

Monthly cost for 81 minutes of call ; x = 81

y = 0.09(81) + 12.18

y = 7.29 + 12.18

y = 19.47

Answer 2

$19.47

1) Examining the graph, we can write two coordinate pairs the x-coordinate for the minutes and the y-coordinate for the cost. So we have (54, 17.04) and (86, 19.92) so we can find from that the rule of this function. Let's find the slope of it:

`m=(y_2-y_1)/(x_2-x_1)=(19.92-17.04)/(86-54)=0.09`

Note that the slope shows how steep is the line of that function.

2) Let's find the linear coefficient, where the graph intercepts the y-axis.

Writing the slope-intercept form:

`\begin{gathered} y=mx+b \\ \mleft(54,17.04\mright) \\ 17.04=0.09(54)+b \\ 17.04-4.86=b \\ b=12.18 \end{gathered}`

So the rule of this function is:

`f(x)=0.09x+12.18`

3) Now we can find out the answer, by plugging into that equation x=81

`\begin{gathered} f(81)=0.09(81)+12.18 \\ f(81)=19.47 \end{gathered}`

Thus, the monthly cost for 81 minutes is $19.47