#### Math - 2019-20

# A.6ab - Slope and Equations

A.6The student willa)

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;

*Adopted: 2016*

### 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. 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_{4 }**Recognize**
and **describe** a line with a slope or
rate of change that is positive, negative, zero, or undefined.

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

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

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

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

·
A.6b_{2 }**Write**
the equation of a line when given two points 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**
the equation of a vertical line as *x*
= *a*.

·
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: Jul 30, 2019*