#### Math - 2017-18

# A.6 and *A.6 - Slope and Linear Equations

**A.6** The student will **graph **linear equations ~~and linear inequalities~~

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)

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

writethe 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

*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_{6} **Recognize** and **describe** a line with a slope that is positive, negative, zero, or
undefined.

·
A.6a_{4 }**Recognize**
and **describe** a line with a slope or
rate of change that is positive, negative, zero, or undefined.

A.6a_{5} **Find**
the slope of a line, given the graph of a line.

·
A.6a_{3 }**Determine**
the slope of a line, given the graph of a line.

A.6a_{3} **Find**
the slope of a line, given the equation of a linear function.

·
A.6a_{1 }**Determine**
the slope of the line, given the equation of a linear function.

A.6a_{4} **Find**
the slope of a line, given the coordinates of two points on the line.

·
A.6a_{2 }**Determine**
the slope of a line, given the coordinates of two points on the line.

A.6b_{1} **Write**
an equation of a line when given the graph of a line.

·
A.6b_{1 }**Write**
the equation of a line when given the graph of a line.

A.6b_{2} **Write**
an equation of a line when given two points on the line whose coordinates are
integers.

·
A.6b_{2 }**Write**
the equation of a line when given two points on the line whose coordinates are
integers.

A.6b_{3} **Write**
an equation of a line given the slope and a point on the line whose coordinates
are integers.

·
A.6b_{3 }**Write**
the equation of a line when given the slope and a point on the line whose
coordinates are integers.

A.6b_{4} **Write**
an equation of a vertical line as x = a

·
A.6b_{4 }**Write**
the equation of a vertical line as *x*
= *a*.

A.6b_{5} **Write**
an equation of a horizontal line as y = c

·
A.6b_{5 }**Write**
the equation of a horizontal line as *y*
= *c*.

·
A.6b_{6 }**Write**
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*