Math 101 Intermediate Algebra    Slope-Intercept and Point-SlopeForms 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 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 (x1, y1) from the equation. Plot the point (x1, y1). Write the slope as a rational number, m = c/d. 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. Draw a straight line through the two points.