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Intermediate Algebra chapter 3 part 3

__Slope-Intercept and Point-Slope__

Forms of a Linear EquationChapter 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 - y
_{1} = m(x - x_{1}) - where
- m is the slope
- the point (x
_{1}, y_{1}) is a specified point on the line.

- Use when:
- given two points
- calculate the slope, m, between the two points
- 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:
- Determine the slope of each line.
- The lines are parallel if the slopes are equal.
- The lines are perpendicular if the product of the slopes is -1.
- Otherwise, the lines are neither parallel nor perpendicular.

**Graphing from Slope-Intercept Form**
- Read the slope m and y-intecept (0, b) from the equation.
- Plot the y-intecept (0, b).
- Write the slope as a rational number, m = c/d.
- 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.

- Draw a straight line through the two points.

**Graphing from Point-Slope Form**
- Read the slope m and point (x
_{1}, y_{1}) from the equation.
- Plot the point (x
_{1}, y_{1}).
- Write the slope as a rational number, m = c/d.
- Starting at the point (x
_{1}, y_{1}), 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.

- Draw a straight line through the two points.

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