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Week 6: Algebra - Functions

Triangle from a Line (Printable PDF)

The line Ax + By = C will form a triangle with the x and y axis for what values of A, B, and C?



As seen in problem exploration

M7N1: Students will understand the meaning of positive and negative numbers including rational numbers and will compute with them.

c. Add, subtract, multiply and divide positive and negative rational numbers.

A, B, and C can be negative values as well as rational and graphing these equations requires an understanding of these concepts.

M7A3: Students will understand relationships between two variables.

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

Ax + By = C represents a linear function. By graphing and evaluating the equation, students will work with linear equations. Vertical and horizontal lines may also be discussed in terms of functions and relations.

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 (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.

d. Graph equations of the form ax + by = c.

b. Students must graphically represent equations in the form Ax+By=C and analyze whether or not the graph forms a triangle between the x and y axis.

d. The concept of intercept is essential for the discussion in order to create a triangle with the x- and y-axis, the intercepts must be something other than zero.