Proportionality. The student applies mathematical process standards to use proportional relationships to describe dilations. The student is expected to:
(A) generalize that the ratio of corresponding sides of similar shapes are proportional, including a shape and its dilation;
(B) compare and contrast the attributes of a shape and its dilation(s) on a coordinate plane; and
(C) use an algebraic representation to explain the effect of a given positive rational scale factor applied to two-dimensional figures on a coordinate plane with the origin as the center of dilation.
Proportionality. The student applies mathematical process standards to explain proportional and non-proportional relationships involving slope. The student is expected to:
(A) use similar right triangles to develop an understanding that slope, m, given as the rate comparing the change in y-values to the change in x-values, (y2 - y1)/ (x2 - x1), is the same for any two points (x1, y1) and (x2, y2) on the same line;
(B) graph proportional relationships, interpreting the unit rate as the slope of the line that models the relationship; and
(C) use data from a table or graph to determine the rate of change or slope and y-intercept in mathematical and real-world problems.
(5) Proportionality. The student applies mathematical process standards to use proportional and nonproportional relationships to develop foundational concepts of functions. The student is expected to:
(A) represent linear proportional situations with tables, graphs, and equations in the form of y = kx;
(B) represent linear non-proportional situations with tables, graphs, and equations in the form of y = mx + b, where b ≠ 0;
(C) contrast bivariate sets of data that suggest a linear relationship with bivariate sets of data that do not suggest a linear relationship from a graphical representation;
(D) use a trend line that approximates the linear relationship between bivariate sets of data to make predictions;
(E) solve problems involving direct variation;
(F) distinguish between proportional and non-proportional situations using tables, graphs, and equations in the form y = kx or y = mx + b, where b ≠ 0;
(G) identify functions using sets of ordered pairs, tables, mappings, and graphs; (H) identify examples of proportional and non-proportional functions that arise from mathematical and real-world problems; and
(I) write an equation in the form y = mx + b to model a linear relationship between two quantities using verbal, numerical, tabular, and graphical representations.