generalize that the ratio of corresponding sides of similar shapes are proportional, including a shape and its dilation

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generalize that the ratio of corresponding sides of similar shapes are proportional, including a shape and its dilation

compare and contrast the attributes of a shape and its dilation(s) on a coordinate plane

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

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

graph proportional relationships, interpreting the unit rate as the slope of the line that models the relationship

use data from a table or graph to determine the rate of change or slope and y-intercept in mathematical and real-world problems

represent linear proportional situations with tables, graphs, and equations in the form of y = kx

represent linear non-proportional situations with tables, graphs, and equations in the form of y = mx + b, where b ≠ 0

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

use a trend line that approximates the linear relationship between bivariate sets of data to make predictions

solve problems involving direct variation

distinguish between proportional and non-proportional situations using tables, graphs, and equations in the form y = kx or y = mx + b, where b ≠ 0

identify functions using sets of ordered pairs, tables, mappings, and graphs

identify examples of proportional and non-proportional functions that arise from mathematical and real-world problems

write an equation in the form y = mx + b to model a linear relationship between two quantities using verbal, numerical, tabular, and graphical representations