Open Middle®
Directions: Complete the table & graph below
or here on Desmos to create a linear relation. Find the equation of the linear relation.
Fill in the table again and again to create as many different linear relations as you can.
What do the graphs have in common? What do the equations have in common?
Hint
You get to create any pattern you like….put one point in. What pattern have you started between the points?
Answer
possible answers (infinite):
y = 3x + 3
y = 1/2x + 3
y = 2x + 3
y = -2x + 3
y = 3x + 3
y = 1/2x + 3
y = 2x + 3
y = -2x + 3
The graphs all have the same y-intercept, and therefore have the same constant.
Source: Jon Orr
After the students got started and were writing the equations, I started to tell the students the type of slope they needed to find next. I would say find a slope that is a negative improper fraction, a positive integer or 0. I felt this made the students come up with a better understanding of slope.