# Chapter 3: Slope Intercept Form

Chapter 3: Slope Intercept Form

Rate of Change and Slope:

1) Fill in the table with the missing value.
x / y
1 / 4
5
5 / 4
7 / 3
/ 2) Triangles ABC and CDE are shown on the coordinate plane.
Fill in the blanks with line segments on the graph to make a true statement.
The slope of line segment AC is ______to the slope of line segment CE because the ratio of _____ to _____ is equal to the ratio of ______to ______.
3) The table shows the amount of money, in dollars, Tasha has after purchasing a certain number of songs. Each song costs the same amount.
Number of Songs / Amount of Money Tasha Has (\$)
2 / 27.60
3 / 26.40
4 / 25.20
Fill in the blanks with the correct values.
According to the table, Tasha initially had \$ ______before purchasing songs, and the cost of each song was \$ ______. / 4) The graph shows the relationship between the value of a car, in dollars, after t years. Which statements are true about the relationship? Select all that apply.

A) After 10 years, the car is worth \$0.
B) The value of the car increases by \$1,200 each year.
C) The value of the car decreases by \$1,200 each year.
D) The value of the car when it was brand new was \$16,600.
E) The relationship can be modeled by the linear function
5) Find the slope between the set of points. / 6) Find the slope between the set of points.

Slope-Intercept Form:

7) Bruce rents snowmobiles to tourists. He charges \$135 for 4 hours and \$202.50 for 6 hours. What is the hourly rate Bruce charges to rent a snowmobile? Then write an equation to represent this situation.
8) The equation models the approximate height of a plant in centimeters after x weeks. Complete the following sentences.
1. The plant grows a total ______cm.
1. The initial height of the plant is ______cm.
/ 9) Write the equation in slope intercept of the line that passes through the points (0, 1) and (2, 5).
10) Eric planted a seedling in his garden and recorded its height each week. The equation shown can be used to estimate the height, h, in inches, of the seedling by the end of each week, w, after it was planted. The equation is used to represent the seedling.
1. Explain each part of the equation.
1. If the seedling is 8.25 inches, how many weeks did it take?
/ 11) Write the equation in slope intercept of the line that passes through the points (-5, 9) and (1, 3).
12) Line t is shown in the coordinate plane.
1. Write the equation of the line in slope-intercept form.
/
1. Line s (not shown) has the same slope and passes through the point (0, 4). Which table represents 4 points on line s?
/
1. Write an equation that could represent line s.

Solving Systems of Equations:

13) A linear equation is graphed on the coordinate plane shown.

When graphed on the same coordinate plane, which equation results in a system of equations with exactly one solution?
/ 14) Determine the solution to the system of equations.

15) In this system of equations, determine a solution.
/ 16) Consider the system of equations.

Which statements are true about the system of equations? Select each correct answer.
1. The graph of the system consists of lines that have no points of intersection.
2. The graph of the system consists of lines that have exactly one point of intersection.
3. The graph of the system consists of lines that have more than one point of intersection.
4. The system has no solution.
5. The system has exactly one solution.
6. The system has more than more than one solution.

17) Write and solve a system of equations that represents each situation. Interpret the solution. Morgan is 15 years younger than Mrs. Santos. Their combined age is 44.
/ 18) Write and solve a system of equations that represents each situation. Interpret the solution. The total number of cats and dogs at the shelter is 125. There are 5 more cats than dogs.
19) Write and solve a system of equations that represents each situation. Interpret the solution. The perimeter of a rectangle is 36 meters. The length of the rectangle is 4 meters longer than the width. Find the length and width of the rectangle. / 20) Write and solve a system of equations that represents each situation. Interpret the solution. Amal worked a total of 30 hours last week. On Saturday and Sunday he worked 5 times as many hours than he worked the rest of the week. How many hours did he work the rest of the week?