A.6a and *A.6c - Linear Equations

A.6    The student will graph linear equations and linear inequalities in two variables, including

a)  determining the slope of a line when given an equation of the line, the graph of the line, or two points on the line.  Slope will be described as rate of change and will be positive, negative, zero, or undefined;

A.6  The student will

c)   graph linear equations in two variables.

Bloom's Level:  Apply

BIG IDEAS

• I can master the challenge of a ski slope for snowboarding, determine the gradient of a road, figure the pitch of a roof, and build a handicap accessible ramp to a door.
• I will understand slope is rate of change where one value changing proportionately effects the other value, and the pattern of this relationship can be represented by a line that facilitates analysis and prediction.

UNDERSTANDING THE STANDARD

• Changes in slope may be described by dilations or reflections or both.
• Changes in the y-intercept may be described by translations.
• Linear equations can be graphed using slope, x- and y-intercepts, and/or transformations of the parent function.
• The slope of a line represents a constant rate of change in the dependent variable when the independent variable changes by a  constant amount.
• The equation of a line defines the relationship between two variables.
• The graph of a line represents the set of points that satisfies the equation of a line.
• A line can be represented by its graph or by an equation.
• The graph of the solutions of a linear inequality is a half-plane  bounded by the graph of its related linear equation.  Points on the boundary are included unless it is a strict inequality.
• Parallel lines have equal slopes.
• The product of the slopes of perpendicular lines is -1 unless one of the lines has an undefined slope.

·  Changes in slope may be described by dilations or reflections or both.

·  Changes in the y-intercept may be described by translations.

·  Linear equations can be graphed using slope, x- and y-intercepts, and/or transformations of the parent function.

·  The slope of a line represents a constant rate of change in the dependent variable when the independent variable changes by a constant amount.

·  The equation of a line defines the relationship between two variables.

·  The graph of a line represents the set of points that satisfies the equation of a line.

·  A line can be represented by its graph or by an equation. Students should have experiences writing equations of lines in various forms, including standard form, slope-intercept form, or point-slope form.

·  Parallel lines have equal slopes.

·  The product of the slopes of perpendicular lines is -1 unless one of the lines has an undefined slope.

·  Slope can be described as a rate of change and will be positive, negative, zero, or undefined.

ESSENTIALS

The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

A.6a1  Graph linear equations in two variables, including those that arise from a variety of real-world problems.

·  A.6cGraph a linear equation in two variables, including those that arise from a variety of practical situations.

A.6a2  Use the parent function y = x and describe transformations defined by changes in the slope or y-intercept.

·  A.6cUse the parent function y = x and describe transformations defined by changes in the slope or y-intercept.

A.6a7  Use transformational graphing to investigate effects of changes in equation parameters on the graph of the equations.

KEY VOCABULARY

parent function, transformations, slope, intercepts, coordinates, graph, positive slope, negative slope, zero slope, undefined slope, equation of a line, vertical, horizontal, dilations, reflections, translation, rate of change, dependent variable, independent variable, boundary, parallel, perpendicular

Updated: Oct 27, 2017