# Graphs and Linear Equations

1. The following table shows the height of a tree as it ages. In Excel, plot each point on the same graph where the first coordinate is the age of the tree and the second coordinate is the height of the tree (age, height). After plotting each point, explain if there is a linear relationship between the age and height of the tree.

Age (years) 5 10 15 20 25

Height (ft) 10 12.5 17.5 21 16

Graph:

Explanation of linear relationship:

Describe what might have happened to the tree at age 25.

2. Graph the following equations.

A.

Graph:

B.

Graph:

3. Answer the following questions pertaining to the following graph.

A. Give a brief explanation describing the graph in terms of its x-axis and y-axis.

B. At what age was the number of hours of television watched the most?

C. Find the slope of the line. Show all work to receive full credit.

D. Write a sentence that explains the meaning of the slope.

E. Find the equation of the line that represents the number of hours of television watched. Show all work to receive full credit.

4. The equation represents the total cost to run Johnny's Pizza place for a day. C symbolizes the total cost to open the pizza place, and x stands for the number of pizzas sold.

A. Find the y-intercept of this graph and explain what it means in the context of the problem. Show all work to receive full credit.

B. Explain the slope of the line.

C. Graph the equation.

5. The director of a summer day camp estimates that 100 children will join if the camp fee is $250, but for each $20 decrease in the fee, ten more children will enroll.

A. Determine the linear equation that will represent the number of children who will enroll at a given fee. Hint: To write the slope, you need two points on the line. Show all work to receive full credit.

B. Graph the linear equation that represents the number of children who will enroll at a given fee.

C. Approximately how many students will enroll if the camp fee is $180? Round to the nearest child.

D. Approximately how many students will enroll if the camp is free? Round to the nearest child.

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#### Solution Summary

Graphs and Linear Equations are investigated.