Math - 2019-20
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.
- 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
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. 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.
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to
and describe a line with a slope or
rate of change that is positive, negative, zero, or undefined.
the slope of a line, given the graph of a line.
the slope of the line, given the equation of a linear function.
the slope of a line, given the coordinates of two points on the line.
the equation of a line when given the graph of a line.
the equation of a line when given two points on the line whose coordinates are
the equation of a line when given the slope and a point on the line whose
coordinates are integers.
the equation of a vertical line as x
the equation of a horizontal line as y
· A.6b6 Write 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.
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