# A.6 - Graph Linear Equations

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;

c)   graph linear equations in two variables.

### 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

2016 VDOE Curriculum Framework - AI.6 Understanding

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

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

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

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

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

·  A.6bWrite the equation of a line when given two points 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.6bWrite the equation of a vertical line as x = a.

·  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.

·  A.6c1 Graph a linear equation in two variables, including those that arise from a variety of practical situations.

·  A.6c2 Use the parent function y = x and describe transformations defined by changes in the slope or y-intercept.

### 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: Aug 23, 2018