[MA2015] (8) 13 :
13 ) Interpret the equation y = mx + b as defining a linear function whose graph is a straight line; give examples of functions that are not linear. [8-F3]
Example: The function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4), and (3,9), which are not on a straight line.
[MA2019] REG-8 (8) 8 :
8. Graph proportional relationships.
a. Interpret the unit rate of a proportional relationship, describing the constant of proportionality as the slope of the graph which goes through the origin and has the equation y = mx where m is the slope. [MA2019] REG-8 (8) 9 :
9. Interpret y = mx + b as defining a linear equation whose graph is a line with m as the slope and b as the y-intercept.
a. Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in a coordinate plane.
b. Given two distinct points in a coordinate plane, find the slope of the line containing the two points and explain why it will be the same for any two distinct points on the line.
c. Graph linear relationships, interpreting the slope as the rate of change of the graph and the y-intercept as the initial value.
d. Given that the slopes for two different sets of points are equal, demonstrate that the linear equations that include those two sets of points may have different y-intercepts. [MA2019] REG-8 (8) 12 :
12. Solve systems of two linear equations in two variables by graphing and substitution.
a. Explain that the solution(s) of systems of two linear equations in two variables corresponds to points of intersection on their graphs because points of intersection satisfy both equations simultaneously.
b. Interpret and justify the results of systems of two linear equations in two variables (one solution, no solution, or infinitely many solutions) when applied to real-world and mathematical problems. [MA2019] REG-8 (8) 13 :
13. Determine whether a relation is a function, defining a function as a rule that assigns to each input (independent value) exactly one output (dependent value), and given a graph, table, mapping, or set of ordered pairs. [MA2019] REG-8 (8) 15 :
15. Compare properties of functions represented algebraically, graphically, numerically in tables, or by verbal descriptions.
a. Distinguish between linear and non-linear functions.