Activities

1. Look at the line graphed below. What is the equation of the line?

2. Write the equation 2x – 3y = -9 in slope intercept form.

3. The slope of a line is -6. The line goes through the point (7, -14). Write the equation of the line in point-slope form.

4. What is the equation of the line, in slope-intercept form, that passes through the points (2, 4) and (3, 4)?

5. What is the equation of the line graphed below?

6. What is the equation of the line that connects the points (3, 7) and (-6, 1)?

7. The linear equation goes through the points (5, a) and (-15, b). What are the values of a and b?

8. What is the equation of the line graphed here:

9. Write the linear equation that passes through (-2, -5) and (2, 7) in point slope, slope-intercept and standard forms.

10. Identify the equations of lines A, B, and C.

11. What is the slope and one point that the line 5x – 6y = 15 passes through?

12. What is the equation of the line that passes through (4, -9), and (-2, 9)?

13. The rate of change for a linear function is -62 miles per hour. If your car is 589 miles away from home after 5 hours of driving towards your house, what is the linear equation that represents the distance from your house (d) after driving for a number of hours (h)?

14. A pizza with 3 toppings costs $12.45. A pizza with 7 toppings costs $17.05. What is the equation that determines the cost of a pizza (c) based on the number of toppings (t)?

15. The graph below shows the number of people remaining inside a commercial building (p) based on the number of minutes after closing time (m). What is the equation represented by the graph?

16. Look at the following equations. Determine if the equations are linear functions or not.

a. x = 1                        b. 3y + 7 – x² = 2(4 – 0.5x²)                c.            d. y + x = x + y

17. The line x = 3 is a straight line, but not a linear function, why?

18. What is the equation of the line between and ?

19. The equation of a line goes through the point (a, b) and has slope c. What is the slope-intercept equation of the line?

20. What is the equation, in standard form, of a line that is parallel to 3x – 4y = 11.5 and passes through the coordinate point (120, -99)?

21. Two lines pass through the point (5, -4). The first line also goes through (6, 7) and the second line also passes through (4, -10). What is the sum of the slopes of the two lines?

22. A line passes through (a + 7, b) and (a, b – 4) what could be the equation of the line?

23. A line is found only in quadrants II and IV. What could be the equation of the line?

24. Sam has been thinking about his own growth recently. He is trying to estimate the slope and y-intercept for a linear equation representing his growth from birth to the end of puberty. What advice can you give Sam regarding his linear equation?

25. Look at the graph below. What could be the equations of lines A, B, C, and D?

Answer Key/Rubric

3. y + 14 = -6(x – 7)

4. y = 0x + 4

7. a = 4, b = 16

8. y = 7x – 26

9. Point Slope: y – 7 = 3(x – 2), Slope-intercept:  y = 3x + 1, Standard: -3x + y = 1

10. A: y = 2x + 3, B: y = 7x – 2, C: y = -x -8

11. Slope: One point that the line passes through: (3, 0)

12. y = -3x + 3

13. d = -62h + 899

14. c = 1.15t + 9

16. a. No, b. Yes, c. No, d. No

17. The line x = 3 is not a linear function because it is not a function. There is more than one output for the input of x = 3.

19. y = cx + (b – ca)

20. -3x + 4y = -756

21. 17

22. Various answers but must have the slope:

23. Various answers but must have this y-intercept y = 2x + 0

24. First, he needs to decide to use inches, not feet for his equation. Next, Sam should realize that around 20 inches would be the starting point for this equation because most babies are born at that height. Lastly, the number of inches per year growth would be the difference from their current height to their initial height divided by their age. A number around 3 inches per year might be close for many people.
    
    
25. A: , B: y = 7x + 30, C: y = 0x + 1, D: y = -x – 4