Lines

HamiltonCityABLE, Jan 15, 2016

A set of worksheets for exploring lines and linear equations.

Table of Contents

  1. The Coordinate Plane
    1. Moving a Point on the Coordinate Grid
    2. Points in the Four Quadrants and on the Axes
    3. A Point's Distance from the Axes
  2. Slope of a Line
    1. Distance Between Two Points
    2. Exploring the Slope of a Line
    3. Exploring the Slope and the y-intercept of a Line
  3. Forms of a Linear Equation
    1. The Slope-Intercept Form of a Linear Equation
    2. The Point-Slope Form of a Linear Equation
    3. Graph the Line (Easier)
    4. Graph the Line (Harder)
    5. Graph the Line (Even Harder)
  4. Equations for Parallel and Perpendicular Lines
    1. Equations of Parallel Lines
    2. Equations of Perpendicular Lines

1.

The Coordinate Plane

  • 1. Moving a Point on the Coordinate Grid
  • 2. Points in the Four Quadrants and on the Axes
  • 3. A Point's Distance from the Axes

1.1.

Moving a Point on the Coordinate Grid

Move around the point.[br][br]See how its [math]x[/math] and [math]y[/math] value change as its location changes.
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1.2.

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1.3.

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2.

Slope of a Line

  • 1. Distance Between Two Points
  • 2. Exploring the Slope of a Line
  • 3. Exploring the Slope and the y-intercept of a Line

2.1.

Distance Between Two Points

Move Point A or B. Notice how the distance between the two points changes.
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2.2.

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2.3.

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3.

Forms of a Linear Equation

  • 1. The Slope-Intercept Form of a Linear Equation
  • 2. The Point-Slope Form of a Linear Equation
  • 3. Graph the Line (Easier)
  • 4. Graph the Line (Harder)
  • 5. Graph the Line (Even Harder)

3.1.

The Slope-Intercept Form of a Linear Equation

The slope-intercept form of a linear equation is [math]y = mx +b[/math]. Move slider [math]m[/math]. See the steepness of the line change. The slope of the line is [math]m[/math]. When [math]m[/math] is negative, the direction of the line changes. When [math]m = 0[/math], the line is flat. Vertical lines do not have a slope. Where the line intersects the [math]y[/math]-axis is the [math]y[/math]-intercept point of the line. The [math]y[/math]-intercept is the point [math](0, b)[/math]. Only the [math]b[/math] is used in the equation, and it is the constant term of the equation. Move slider [math]b[/math]. See the line move up or down. When [math]b[/math] is positive, the y-intercept is above the [math]x[/math]-axis. When [math]b[/math] is negative, the y-intercept is below the [math]x[/math]-axis.

To remember the different meaning for different slope values: It is easy to walk across the flat ground. When [math]m=0[/math], it is like flat ground. Some climbs are barely hills, some are challenging hikes, and others require major planning and safety gear. When [math]0<m<1[/math], the climb is barely a hill. When [math]m=1[/math], the slope is 45 degree from the [math]x[/math]-axis and is a challenging hike. When [math]m>1[/math], the line approaches the [math]y[/math]-axis and becomes a major climb requiring planning and safety gear. Only dare devils would scale the side of a skyscraper. The steepness of a vertical line is akin to scaling the side of a skyscraper. The slope does not exist.
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3.3.

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3.4.

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3.5.

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4.

Equations for Parallel and Perpendicular Lines

  • 1. Equations of Parallel Lines
  • 2. Equations of Perpendicular Lines

4.1.

Equations of Parallel Lines

Line [math]a[/math] and Line [math]c[/math] are parallel lines. They have the same slope.[br][br][math]y=mx+b[/math] is the slope-intercept form of a linear equation.[br]The slope is [math]m[/math].[br][br]Move slider [math]m[/math]. The slope for both lines will change. [br][br]Move slider [math]b[/math]. Line [math]a[/math] will move, but line [math]c[/math] will be stationary.
Equations of Parallel Lines
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