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Week 6: Algebra - Functions

Modifying the Slope and Y-Intercept (Printable PDF)

A linear function (a function that graphs as a line) can be written in the form f(x) = mx + b, where m and b are real numbers.
If x is fixed, what happens to the value of f(x) if m increases by one? if m decreases by two? if m changes by n?
If x is fixed, what happens to the value of f(x) if b increases by one? if b decreases by two? if b changes by n?



As seen in Problem Exploration

M6A2: Students will consider relationships between varying quantities.

a. Analyze and describe patterns arising from mathematical rules, tables, and graphs.
By exploring this linear function, the student is exploring the relationship between two quantities. This can be done by analyzing a graph of linear functions.
M7A3: Students will understand relationships between two variables.

b. Represent, describe and analyze relations from tables, graphs, and formulas
By graphing and evaluating the linear equations, students will be representing, describing and analyzing functional relations from graphs.
M8A3: Students will understand relations and linear functions.

j. Translate among verbal, tabular, graphic, and algebraic representations of functions.
The student must be able to translate between the algebraic representation of the functions 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.
Linear equations are being graphed and analyzed in this investigation. They are all written in the form of y=mx+b. The analysis in this investigation involves seeing what happens to a graph when the slope and y-intercept are changed.