154k views
3 votes
Emma rides her bike at a constant speed. The table shows her data. % Number of G f 누 f Minutes 10 30 40 20 80 50 60 70 Number of 25 Miles 1.2 B 2.4. 3.6 7.2 8.4 G 4.8 6.0 9.6 (y) Part A Describe a linear function for the number of miles Emma rides her bike in 3 minutes. Type your answer in the box below. The number of miles Emma rides is a function of the number of she rides.

User Raugfer
by
8.6k points

1 Answer

5 votes

We are given a table of values between the number of miles (y) and the number of minutes (x)

A linear function is given by


y=mx+b

Where m is the slope and b is the y-intercept.

The slope is given by


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

Choose any two (x, y) pairs from the given table.

Let us choose (10, 1.2) and (30, 3.6)


(x_1,y_1)=(10,1.2)\: \text{and}\: (x_2,y_2)=(30,3.6)

Let us substitute these points into the above slope formula.


m=(y_2-y_1)/(x_2-x_1)=(3.6-1.2)/(30-10)=(2.4)/(20)=0.12

So, the slope is 0.12


y=0.12x+b

To find the y-intercept (b), choose any one point from the given table

Let us choose (10, 1.2) and substitute it into the above equation


\begin{gathered} y=0.12x+b \\ 1.2=0.12(10)+b \\ 1.2=1.2+b \\ 1.2-1.2=b \\ 0=b \\ b=0 \end{gathered}

So, the y-intercept is 0

Therefore, the linear function for the given relationship is


y=0.12x

You can find the number of miles (y) Emma rides by substituting the number of minutes (x) into function.

User Nhoxbypass
by
7.8k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.