Linear Functions - Reporting Category 3
Linear functions. The student understands that linear functions can be represented in different ways and translates among their various representations. The student understands the meaning of the slope and intercepts of the graphs of linear functions and zeros of linear functions and interprets and describes the effects of changes in parameters of linear functions in real-world and mathematical situations.
(A.5) Linear functions. The student understands that linear functions can be represented in different ways and translates among their various representations. The student is expected to
(A) determine whether or not given situations can be represented by linear functions; Supporting Standard
- Identify functions (Algebra 1 - Q.4)
- Identify functions: vertical line test (Algebra 1 - Q.5)
- Identify linear functions (Algebra 1 - S.1)
(B) determine the domain and range for linear functions in given situations; and Supporting Standard
(C) use, translate, and make connections among algebraic, tabular, graphical, or verbal descriptions of linear functions. Readiness Standard
- Write a function rule: word problems (Algebra 1 - Q.10)
- Find points on a function graph (Algebra 1 - Q.11)
- Write a rule for a function table (Algebra 1 - Q.12)
- Find the slope of a graph (Algebra 1 - S.2)
- Find slope from two points (Algebra 1 - S.3)
- Slope-intercept form: find slope and y-intercept (Algebra 1 - S.4)
- Slope-intercept form: graph an equation (Algebra 1 - S.5)
- Slope-intercept form: write an equation from a graph (Algebra 1 - S.6)
- Slope-intercept form: write an equation (Algebra 1 - S.7)
- Linear function word problems (Algebra 1 - S.9)
- Write equations in standard form (Algebra 1 - S.10)
- Standard form: find x- and y-intercepts (Algebra 1 - S.11)
- Standard form: graph an equation (Algebra 1 - S.12)
- Equations of horizontal and vertical lines (Algebra 1 - S.13)
- Graph a horizontal or vertical line (Algebra 1 - S.14)
- Point-slope form: graph an equation (Algebra 1 - S.15)
- Point-slope form: write an equation from a graph (Algebra 1 - S.16)
- Point-slope form: write an equation (Algebra 1 - S.17)
- Slopes of parallel and perpendicular lines (Algebra 1 - S.18)
- Write an equation for a parallel or perpendicular line (Algebra 1 - S.19)
(A.6) Linear functions. The student understands the meaning of the slope and intercepts of the graphs of linear functions and zeros of linear functions and interprets and describes the effects of changes in parameters of linear functions in real-world and mathematical situations. The student is expected to
(A) develop the concept of slope as rate of change and determine slopes from graphs, tables, and algebraic representations; Supporting Standard
- Rate of change (Eighth grade - H.11)
- Constant rate of change (Eighth grade - H.12)
- Find the slope of a graph (Algebra 1 - S.2)
- Find slope from two points (Algebra 1 - S.3)
- Slope-intercept form: find slope and y-intercept (Algebra 1 - S.4)
- Slopes of parallel and perpendicular lines (Algebra 1 - S.18)
(B) interpret the meaning of slope and intercepts in situations using data, symbolic representations, or graphs; Readiness Standard
- Identify proportional relationships (Algebra 1 - R.1)
- Find the constant of variation (Algebra 1 - R.2)
- Linear function word problems (Algebra 1 - S.9)
(C) investigate, describe, and predict the effects of changes in m and b on the graph of y = mx + b; Readiness Standard
(D) graph and write equations of lines given characteristics such as two points, a point and a slope, or a slope and y-intercept; Supporting Standard
- Find slope from two points (Algebra 1 - S.3)
- Slope-intercept form: graph an equation (Algebra 1 - S.5)
- Slope-intercept form: write an equation from a graph (Algebra 1 - S.6)
- Slope-intercept form: write an equation (Algebra 1 - S.7)
- Write equations in standard form (Algebra 1 - S.10)
- Standard form: graph an equation (Algebra 1 - S.12)
- Equations of horizontal and vertical lines (Algebra 1 - S.13)
- Graph a horizontal or vertical line (Algebra 1 - S.14)
- Point-slope form: graph an equation (Algebra 1 - S.15)
- Point-slope form: write an equation from a graph (Algebra 1 - S.16)
- Point-slope form: write an equation (Algebra 1 - S.17)
- Write an equation for a parallel or perpendicular line (Algebra 1 - S.19)
(E) determine the intercepts of the graphs of linear functions and zeros of linear functions from graphs, tables, and algebraic representations; Supporting Standard
- Slope-intercept form: find slope and y-intercept (Algebra 1 - S.4)
- Standard form: find x- and y-intercepts (Algebra 1 - S.11)
(F) interpret and predict the effects of changing slope and y-intercept in applied situations; and Readiness Standard
(G) relate direct variation to linear functions and solve problems involving proportional change. Supporting Standard
- Unit rates (Algebra 1 - C.3)
- Unit prices (Algebra 1 - C.4)
- Solve proportions (Algebra 1 - C.5)
- Solve proportions: word problems (Algebra 1 - C.6)
- Scale drawings and scale factors (Algebra 1 - C.7)
- Find the constant of variation (Algebra 1 - R.2)
- Graph a proportional relationship (Algebra 1 - R.3)
- Write direct variation equations (Algebra 1 - R.4)
- Write and solve direct variation equations (Algebra 1 - R.5)