Open Middle®
Directions: Using the integers -4 to 4, at most one time each, create a system of linear equations that has a solution in quadrant 4.
x | y
——
_ | _
_ | _
_ | _
and
y = _ / _ x + _
Hint
Where is quadrant 4?
How does the slope of the line in slope-intercept form affect which quadrants it will go through?
How does the y-intercept of the line in slope-intercept form affect which quadrants it will go through?
What restrictions are there for placing values in the table so that they have a linear relationship?
Here is a visual representation of the answer on Desmos.
How does the slope of the line in slope-intercept form affect which quadrants it will go through?
How does the y-intercept of the line in slope-intercept form affect which quadrants it will go through?
What restrictions are there for placing values in the table so that they have a linear relationship?
Here is a visual representation of the answer on Desmos.
Answer
One answer is
y= (-1 / 4) x+-3
and
x | y
——
1 | -4
2 | -2
3 | 0
Here is a visual representation of the answer on Desmos.
Source: Robert Kaplinsky
I’m going to try this problem for students who are just learning to recognize the characteristics of linear functions. They will only have to create one equation and also the table of values using the same restrictions.