Question

8. A plane uses a certain amount of fuel based on the number of miles it travels as shown in thetable.Miles Traveled 0 30 60 90 120Gallons of Fuel0156312468624a. What is the slope of the table, and what does it mean in the situation?b. What is the y-intercept of the table, and what does it mean in the situation?c. Write an equation for the table.

Answer 1

Remember the formua to calculate the slope of a line between to points

`\begin{gathered} A(x_1,y_1) \\ \text{and} \\ B(x_2,y_2) \end{gathered}`

is:

`m=(y_2-y_1)/(x_2-x_1)`

So to calculate the slope of the table, let's use the points

A(0 , 0) and B(30 , 156). Thus,

`\begin{gathered} m=(156-0)/(30-0)\rightarrow m=(156)/(30) \\ m=5.2 \end{gathered}`

You can check that this slope works for any consecutive pair of points of the table, since the data is related with a straight line (constant slope)

To get a better sense of what a slope means, let's think about the original units of measurement of the data. Notice that the units for x data is "Miles traveled" and the units for y data is "Gallons of fuel".

In the formula for slope, we divide y data by x data. Therefore, the whole slope, with units of measurement, would be

`m=5.2\text{ }\frac{\text{Gallons of fuel}}{\text{Mile(s) traveled}}`

Thus, the slope of the table would mean the gallons of fuel consumed per each mile traveled

Now, remember the y-intercept occurs when x = 0.

In this case, the y-intercept would be 0, meaning that the plane didn't use any fuel until it started the journey. Perhaps it was parked and with the engines off.

To come up with an equation for the table, lets use the slope we calculated, point A(0 , 0) and the slope-point form of a line, as following:

`\begin{gathered} y-0=5.2(x-0) \\ \rightarrow y=5.2x \end{gathered}`

Answers:

a)

`m=5.2`

The slope of the table means the gallons of fuel consumed per each mile traveled.

b) The y-intercept is 0. It means the plane didn't use any fuel until it started the journey.

c)

`y=5.2x`