Two-Variable Linear Relations

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• Two-variable linear relations using graphing, interpolation and extrapolation
• Two-variable continuous linear relations; includes rational coordinates
• Horizontal and vertical lines
• Graphing relation and analyzing
• Interpolating and extrapolating approximate values
• Spirit canoe journey predictions and daily checks

1. Plot the point (2,-4)
2. y=3x+2
   1. Sketch the line
   2. Slope?
   3. y-intercept?
3. Sketch the line y=-2x+1
4. y=3
   1. Sketch this line
   2. What quadrants is this line in?
5. x=-1
   1. Sketch this line
   2. What quadrants in this line in?
6. Plot the point \left(\frac{1}{2},-3\right)
7. Plot the point \left(-2.\bar{3},2\frac{4}{5}\right)
8. Sketch x=0
9. Sketch y=\pi
10. y=2x+3
    1. Create a table of values
    2. Sketch the graph
    3. State the x-intercept
    4. When x=4, what is the value of y?
11. Given y=mx+b what is the meaning of:
    1. m?
    2. b?
12. Sketch y=2-3x
13. Sketch y=\frac{-2}{3}x+3
14. Sketch y=0.\bar{6}-\frac{x}{3}
15. Sketch x=\pi y
16. Given the points (0,2) and (8,4)
    1. Find the slope
    2. Find the line equation in slope-point form:
       y-y_1=m(x-x_1)
    3. Find the line equation in slope-intercept form:
       y=mx+b
17. Given the points (3,-3) and (-1,-1)
    1. Find the slope
    2. Find the line equation in slope-point form:
       y-y_1=m(x-x_1)
    3. Find the line equation in slope-intercept form:
       y=mx+b
18. Given the point \left(2\frac{1}{2},-\frac{1}{2}\right) and \left(4,-2\frac{1}{4}\right) find the slope
19. You make $50 for showing up to your job site and you charge $40 per hour
    1. What is the equation of the graph?
    2. Sketch this graph
    3. How much do you make for working 8 hours?
    4. How long do you have to work to earn $290?
20. Your car burns 6L per 100 km and has a full tank
    of gas of 60L
    1. Write the equation of the Volume distance graph
    2. Sketch this graph
    3. How much fuel do you have left in the tank after
       driving 300 km?
    4. Challenge: What is the meaning of the x-intercept?
    5. Challenge: What is the meaning of the slope of the graph?
21. A canoe starts at 2 km away from home.  Each day the canoe travels 3 more km away from home
    1. Sketch a line graph that models the distance from home
    2. Model this graph as a line equation
    3. How far away is the canoe from home after a
       week?
    4. Interpolate the distance from home after 2.5
       days.
    5. Extrapolate the distance from home after a month
       (4 weeks).
    6. Why is interpolating data more accurate than
       extrapolating data?
22. See figures 1, 2, and 3 below respectively:
    
    1. How many circles are in figure 100?
    2. What figure number contains 131 circles?
23. 10, 7, 4, 1, -2, ... Find the 100th number.
    

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