In Activity we saw earlier, Problem we saw, would it have mattered if your friend had chosen two different points to calculate the slope, such as $(0,0)$ and $(5,100)$ or $(1,20)$ and $(2,40)$ ? Why or why not?

A mile is roughly equivalent one point six kilometers. What linear function relates the number of miles to the number of kilometers? Graph the function. What quantities are proportionally related? Explain.

For each situation, write a sentence that shows how two quantities in the situation are related. It is possible that you can describe several relationships in each situation. a. Joella is going to participate in a run to raise money for cancer research. Her sister pledges 50¢ for every mile that Joella runs. b. For each mile Joella runs, she has total pledges of $12 per mile, all to be matched by an anonymous donor. c. You are making lemonade for a faculty picnic. The juice of a dozen Meyer lemons, 3/4 cup of sugar, and 14 cups of water are needed to make 1 gallon of lemonade.

Draw a graph of the relationship between the number of minutes that have passed and the amount of ice left in the ice block. a. What quantity did you represent on the horizontal axis and what quantity did you represent on the vertical axis? How can this choice reveal important relationships? b. How did you decide on the scale unit? How might the picture of the situation change if the scale unit were different? Notes c. Where on the graph does it indicate when the block of ice will be gone?

For the following functions, complete the input-output tables. Use that information to decide whether or not the function is linear, and tell how you know. If you want to graph the points, you can. In cases where the function is linear, tell what its rate of change is and graph the function. a. $y=x$ b. $y=3$ c. $y=x^2$ d. $y=2 x^2+2 x$

The balance A of a savings account that earns compound interest is expressed with the following $A=P(1+r)^{r t} . P$ is the principal (amount invested), $r$ is the rate per compounding period, $t$ is the time in years, and $n$ is the number of compound periods each year. Use the formula for compound interest to find the balance if $\$ 1000$ is invested for one year at the annual interest rate of $5 \%$ compounded quarterly.

a. The graph shows a relationship in a bowling situation. Calculate the slope of the line.

b. What does the slope mean in terms of the bowling situation?

c. Draw another line on the graph that has the same slope. What does this line represent in terms of the bowling situation?

d. What is the cost before any games are bowled? What is the y-intercept of the graph? What does the y-intercept mean in terms of the bowling situation?

e. Although such graphs are commonly Number of games bowled used to show the linear pattern of data, why is a solid line literally not appropriate here?

Consider the following problem. A donut machine produces sixty donuts every five minutes. How many donuts does it produce in an hour? a. Identify the rate in this problem. b. What unit ratio is associated with this rate? c. Write a proportion that could be used to find the number of donuts produced in an hour. d. Make a graph of the number of donuts produced every minute. What is the slope of the line? (Remember to put time on the horizontal axis.)

Suppose that Clairisa can run five meters per second and Karlene can run four meters per second. Make a coordinate graph to show the relationship between time and distance from the start. Draw a graph for each runner on the same coordinate system. How are the graphs different? How are they the same?

Determine whether the following pairs of quantities are related to each other. If so, explain whether the value of the quantity given on the right increases or decreases as the value of the corresponding quantity on the left increases.

Activity we saw earlier involves another quantity: the number of cups of soda pop. Is this quantity related as a rate to either the number of containers of water or the number of containers of Secret Formula?

Consider the following situation as described by an elementary school student. A block of ice sits in a tub in the sun. The block of ice consists of Sixteen centiliters of water that have been frozen. The block of ice melts at a rate of three centiliters a minute. Describe in words how these two quantities are related: the size of the block of ice and time.

On the board, put every graph from Activity we saw earlier that differs from others in some way. Then compare them. Are there any graphs that do not make sense? If so, why not? Are there any pairs of graphs that look different from each other but that both make sense? Does there have to be only one correct graph? Explain.

For each of the following functions, complete a table for integer values of x from - 3 to 3. Draw a graph of the data using an appropriate scale. To get an accurate picture of the graph, you'll need to plot a few additional noninteger values for x, such as -2.5, - 1.5, 1.5, and 2.5.

$$\begin{array}{ccc} y = 2x \hspace{35pt}& y = x^2 \hspace{35pt}& y = 2|x|\\ \begin{array}{c|c} x & y\\ \hline -3\\ 0\\ 3\\ \end{array} \hspace{35pt}& \begin{array}{c|c} x & y\\ \hline -3\\ 0\\ 3\\ \end{array} \hspace{35pt}& \begin{array}{c|c} x & y\\ \hline -3\\ 0\\ 3\\ \end{array} \end{array}$$