#### Math - 2017-18

# 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.6The student willc)

graphlinear equations in two variables.

**Bloom's Level:** Apply

*Adopted: 2009*

### 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.

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.6a_{1} **Graph**
linear equations in two variables, including those that arise from a variety of
real-world problems.

·
A.6c_{1 }**Graph**
a linear equation in two variables, including those that arise from a variety
of practical situations.

A.6a_{2} **Use**
the parent function y = x and **describe**
transformations defined by changes in the slope or y-intercept.

·
A.6c_{2 }**Use**
the parent function *y* = *x* and **describe** transformations defined by changes in the slope or *y*-intercept.

A.6a_{7} **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*