Activities

1. Find the slope between these points (2, 3) and (4, 7)?

2. Find the equation of the line between (3, 8) and (4, 11)?

3. Find the y-intercept of the line between the points (2, 5) and (-1, 4)?

4. What is the slope of a line perpendicular to the line passing through (2, 4) and (4, 1)?

5. What is the slope of a line parallel to the line passing through (4, 5) and (2, -1)?

6. Write the equation of a line that has a slope of zero and passes through the point (3, 5)?

7. Graph the equation of the line, 10x – 8y = 16, on the coordinate plane:

8. What is the solution to the equation 2(m - 1) = 3m + 17 ?

9. Determine the slope of the line from the graph.        

10. Determine the equation of this line from the graph.

11. If it is snowing at a rate of half an inch per hour, and there is already 5 inches of snow on the ground, what equation best describes the depth of snow, s, based on the number of hours after it started snowing h?

12. What could be the equation of the line graphed below?

13. Look at the linear equation below:

-1.5x - 10y = 5

What is the value of y when x=y?

14. Jabrina bought a tomato plant that was 8 inches tall. The tomato plant has been growing at a rate of 1.5 inches per week, since she bought it. What is an equation for the height of the plant (H) based on the number of weeks (w)? Why is it unrealistic to have an input value of 100 to plug into this function?
    
    
15. Chris is employed as a waiter in an upscale restaurant. His restaurant pays him $5.75 per hour during which time he can serve two groups. The average tip per group is $8.75. Write an equation that outputs Chris’ total income (I) based on the number of hours he works (h).

16. Create a linear equation with a negative slope that passes through the coordinate point (3, 5).

17. The table shows how many cookies can be made (c) based on the number of sticks of butter (b). Determine how many sticks of butter are required to make 400 cookies.

18. After 11 weeks of owning her new iPhone, Ravyn has 983 pictures on her phone. After a total of 16 weeks, she has a total of 1418 pictures. Assuming she takes the same number of pictures each week, how many pictures were on her phone when she bought it?

19. Explain why there are an infinite number of solutions to the equation below:

4y + 2x – 6 = 3x + 2y – 8

  Give 3 example solutions.

Answer Key/Rubric

1. m = 2
2. y = 3x – 1
3. 13/3 or 4 and 1/3
4. 2/3
5. m = 3
6. y = 5 or y = 0x + 5
7. 
   
8. m = -19
9. m = -3/2
10. 
11. s = 0.5h + 5
12. Various answers including y = -0.5x – 1
13. y = -10/23
14. H = 1.5w + 8, It is unrealistic to have an input of 100 weeks to plug into this function because the tomato plant will stop growing after only a few months.
15. I = h(5.75 + 2(8.75)) = h(5.75 + 17.5) = h(23.25)
16. Various answers including y = -x + 8 (Pick any negative value for the slope and use the equation y – y₁ = m(x – x₁); substitute the value chosen and the point (3, 5))
17. 17 sticks of butter
18. 26 pictures
19. There are infinite solutions to this equation because there are two variables. When one of the variables changes the other variable can change to make the equation true. Three example solutions are: (0, -1), (2, 0), and (4, 1).