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GPS Alignment: Instructor Page
Week 8: Algebra - Graphing


Comparing Lines (Printable PDF)

Let f(x) = ax + b, and g(x) = cx + d, where a, b, c, and d, are any real numbers.
If f(x) and g(x) are graphed, what can you conclude about a, b, c, and/or d, if:

a. f(x) and g(x) are parallel?
b. f(x) and g(x) are perpendicular?
c. f(x) does not cross the x-axis?
d. g(x) is horizontal?
e. f(x) and g(x) have the same y-intercept?

 

GPS As seen in Problem Exploration

M7A3: Students will understand relationships between two variables.

a. Plot points on a coordinate plane.

b. Represent, describe and analyze relations from tables, graphs, and formulas.
 

This investigation requires the student to represent each equation as a graph and then compare and analyze the equations for f(x) and g(x). The student may choose to try different values for a, b, c, and d and to graph those to make connections between these variables and the graphs.
 

M8A3: Students will understand relations and linear functions.

j. Translate among verbal, tabular, graphic, and algebraic representations of functions.
 

The student will translate between the algebraic representation of the functions (equation) and their graphs.

M8A4: Students will graph and analyze graphs of linear equations.

b. Determine the meaning of the slope and y-intercept in a given situation.

c. Graph equations of the form y = mx + b.

e. Determine the equation of a line given a graph, numerical information that defines the line, or a context involving a linear relationship.
 

The student will graph both functions, which are in the form of y=mx + b. The student must also be able to find cases in which the graphs of the two equations meet the given conditions specified in this problem.