Question

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.

Answer 1

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

$m=\frac{y_2-y_1}{x_2-x_1}$

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.

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{3.6-1.2}{30-10}=\frac{2.4}{20}=0.12$

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.