# A.6 and *A.6 - Slope and 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; and

b)  writing the equation of a line when given the graph of the line, two points on the line, or the slope and a point on the line.

A.6  The student will

a)  determine the slope of a line when given an equation of the line, the graph of the line, or two points on the line;

b)  write the equation of a line when given the graph of the line, two points on the line, or the slope and a point on the line;

Bloom's Level:  Apply, Analyze

### 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.6a6  Recognize and describe a line with a slope that is positive, negative, zero, or undefined.

·  A.6aRecognize and describe a line with a slope or rate of change that is positive, negative, zero, or undefined.

A.6a5  Find the slope of a line, given the graph of a line.

·  A.6aDetermine the slope of a line, given the graph of a line.

A.6a3  Find the slope of a line, given the equation of a linear function.

·  A.6aDetermine the slope of the line, given the equation of a linear function.

A.6a4  Find the slope of a line, given the coordinates of two points on the line.

·  A.6aDetermine the slope of a line, given the coordinates of two points on the line.

A.6b1  Write an equation of a line when given the graph of a line.

·  A.6bWrite the equation of a line when given the graph of a line.

A.6b2  Write an equation of a line when given two points on the line whose coordinates are integers.

·  A.6bWrite the equation of a line when given two points on the line whose coordinates are integers.

A.6b3  Write an equation of a line given the slope and a point on the line whose coordinates are integers.

·  A.6bWrite the equation of a line when given the slope and a point on the line whose coordinates are integers.

A.6b4  Write an equation of a vertical line as x = a

·  A.6bWrite the equation of a vertical line as x = a.

A.6b5  Write an equation of a horizontal line as y = c

·  A.6bWrite the equation of a horizontal line as y = c.

·  A.6bWrite the equation of a line parallel or perpendicular to a given line through a given point.

### 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