Math 101 Intermediate Algebra
homechapterstutorialshomework

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

Slope

Slope 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.

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.

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).

Parallel and Perpendicular

Lines 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.

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.

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.