Unit 2 Test Answer Key

1. Which ordered pair represents the origin on the coordinate plane?

• Correct Answer: (0, 0)
• Thought Process: The origin is the point where the x-axis and y-axis intersect, and its coordinates are always (0, 0).

2. Plot the following points on the coordinate plane provided:

• A = (3, -2): Move 3 units right on the x-axis, then 2 units down on the y-axis.
• B = (-1, 4): Move 1 unit left on the x-axis, then 4 units up on the y-axis.
• C = (0, 0): This is the origin.
• D = (-2, -3): Move 2 units left on the x-axis, then 3 units down on the y-axis.
• Thought Process: Students should understand that the first number in an ordered pair is the x-coordinate (horizontal movement) and the second is the y-coordinate (vertical movement).

3. Which of the following graphs represents a function?

• Correct Answer: Graph D (parabola opening up)
• Thought Process: A graph represents a function if it passes the vertical line test, meaning no vertical line intersects the graph at more than one point. A vertical line and a parabola opening left would fail this test.

4. Graph the function $y = 2x - 1$ on the coordinate plane.

• Expected Graph: A straight line with a y-intercept at (0, -1) and a slope of 2 (for every 1 unit right, go 2 units up).
• Thought Process: Students can use the slope-intercept form ($y = mx + b$) to identify the y-intercept (b = -1) and the slope (m = 2). They should plot the y-intercept first, then use the slope to find additional points.

5. Using the vertical line test, determine if the relation shown in the graph below is a function.

• Correct Answer: No, it is not a function.
• Thought Process: If a vertical line can intersect the graph at two or more points, then the graph does not represent a function. The description indicates a vertical line would intersect at two points.

6. Calculate the slope of the line passing through the points (2, 5) and (6, 13).

• Correct Answer: 2
• Thought Process: Use the slope formula: $m = (y_2 - y_1) / (x_2 - x_1)$.
  • $m = (13 - 5) / (6 - 2)$
  • $m = 8 / 4$
  • $m = 2$

7. What is the slope of a horizontal line?

• Correct Answer: 0
• Thought Process: A horizontal line has no vertical change (rise = 0), so the slope is 0 divided by any run, which equals 0.

8. The graph below shows the distance a car traveled over time. Describe what is happening to the car between hours 2 and 4.

• Correct Answer: The car is stopped or not moving.
• Thought Process: On a distance-time graph, a horizontal line segment indicates that the distance is not changing, meaning the object (car) is stationary.

9. A linear function passes through the point (1, 3) and has a slope of -2. Write the equation of this line in slope-intercept form.

• Correct Answer: $y = -2x + 5$
• Thought Process: Use the slope-intercept form $y = mx + b$. We know $m = -2$ and a point (x, y) = (1, 3).
  • Substitute the values into the equation: $3 = -2(1) + b$
  • $3 = -2 + b$
  • Add 2 to both sides: $b = 5$
  • Write the equation: $y = -2x + 5$

10. Which quadrant contains points with a negative x-coordinate and a positive y-coordinate?

• Correct Answer: Quadrant II
• Thought Process:
  • Quadrant I: (+x, +y)
  • Quadrant II: (-x, +y)
  • Quadrant III: (-x, -y)
  • Quadrant IV: (+x, -y)

Unit 2 Review Guide: Coordinate Geometry and Functions

This guide will help you review the key concepts for your upcoming Unit 2 Assessment. Answer the questions and complete the exercises below.

Part 1: The Coordinate Plane

1. Describe how to plot the point (-4, 2) on a coordinate plane. What does each number represent?
   
   
   
   
   
   

2. In which quadrant would the point (5, -3) be located? Explain your reasoning.
   
   
   

3. What are the coordinates of the origin?
   
   
   

Part 2: Functions and the Vertical Line Test

4. Define what a function is in your own words.
   
   
   
   
   
   

5. How do you use the Vertical Line Test to determine if a graph represents a function?
   
   
   
   
   

6. Sketch a graph that is a function and a graph that is not a function.

   • Function:
     
     
     
     
     
     
     
     
     
     
     
     
   • Not a Function:
     
     
     
     
     
     
     
     
     
     
     
     

Part 3: Slope

7. Calculate the slope of the line passing through the points (1, 7) and (3, 11). Show your work.
   
   
   
   
   

8. What does a positive slope indicate about a line?
   
   
   

9. What is the slope of a vertical line? What is the slope of a horizontal line?
   
   
   

Part 4: Interpreting Graphs

10. The graph below shows the temperature of a cup of coffee over time. Describe what is happening to the coffee's temperature between minutes 0-5, 5-10, and 10-15.
    (Imagine a temperature-time graph where the temperature decreases from 0-5, stays constant from 5-10, and decreases again from 10-15)

    • Minutes 0-5:
      
      
      
    • Minutes 5-10:
      
      
      
    • Minutes 10-15:
      
      
      

11. Look at the graph of a linear function $y = -x + 4$. What is the y-intercept and what is the slope?

    • Y-intercept:
      
      
      
    • Slope: