This lesson challenges students to explain the meaning of a solution for a linear combination of two variables with a given constraint and to recognize the solution graphs as a line.
What to look for
Students may note that for equations of the form \(ax+by\) = c where \(a\) and \(b\) are positive, the slope of the "solution line" is always negative.
Sample AssessmentWhich of the following ordered pairs \((x, y)\) is a solution to the equation \(2x+3y = 6\)?
a. (6, 3)
b. (3, 0)
c. (3, 2)
d. (2, 3)
e. (0, 3)