Intermediate Algebra chapter 3 part 3

Slope-Intercept and Point-Slope
Forms of a Linear Equation
Chapter 3

SlopeSlope refers to the slant of a line.
The formula for slope is

Some other renditions of the formula for slope are

A horizontal line has slope of 0.
A vertical line has undefined slope. 

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Slope-Intercept Form of a Linear Equation

The form:   y = mx + b

where

• m is the slope
• the point (0, b) is the y-intercept

Use when:

• given the slope and y-intercept (plug them in).

Any equation of a non-vertical line can be put in slope-intercept form.

• Vertical lines have the form x = a.

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Point-Slope Form of a Linear Equation

The form:   y - y₁ = m(x - x₁)

where

• m is the slope
• the point (x₁, y₁) is a specified point on the line.

Use when:

• given two points
  1. calculate the slope, m, between the two points
  2. plug m and either point into the formula
• given the slope and a point (plug them in).

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Parallel and PerpendicularLines with the same slope are parallel.

• y = 2x - 1
• y = 2x + 3
• m = m = 2
• The red and blue lines are parallel.

Lines with the product of their slopes equal to -1 are perpendicular.

• y = -0.5x + 1
• m·m = -1
• m·m = -1
• The red and blue lines are both perpendicular to the purple line.

To determine if two lines are parallel, perpendicular, or neither:

1. Determine the slope of each line.
2. The lines are parallel if the slopes are equal.
3. The lines are perpendicular if the product of the slopes is -1.
4. Otherwise, the lines are neither parallel nor perpendicular.

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Graphing from Slope-Intercept Form

1. Read the slope m and y-intecept (0, b) from the equation.
2. Plot the y-intecept (0, b).
3. Write the slope as a rational number, m = c/d.
4. Starting at the y-intercept, move c units vertically and then d units horizontally, and plot a point there.
   • c > 0 means up and c < 0 means down.
   • d > 0 means right and d < 0 means left.
5. Draw a straight line through the two points.

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Graphing from Point-Slope Form

1. Read the slope m and point (x₁, y₁) from the equation.
2. Plot the point (x₁, y₁).
3. Write the slope as a rational number, m = c/d.
4. Starting at the point (x₁, y₁), move c units vertically and then d units horizontally, and plot a point there.
   • c > 0 means up and c < 0 means down.
   • d > 0 means right and d < 0 means left.
5. Draw a straight line through the two points.