Linear Equations and Slope Created by Laura Ralston

b v=J_U93-l5Z-w v=J_U93-l5Z-w v=J_U93-l5Z-w

Slope in Real Life Grade for Roads Pitch of Building Roofs

Slope b a useful measure of the “steepness” or “tilt” of a line b compares the vertical change (the rise) to the horizontal change (the run) when moving from one point to another along the line b typically represented by “m” because it is the first letter of the French verb, monter

Formula and Graph D1RiNs

Four Possibilities of Slope b Positive Slope m > 0 m > 0 b Line “rises” from left to right b Negative Slope m < 0 b Line “falls” from left to right

Four Possibilities of Slope b Zero Slope m = 0 m = 0 b Line is horizontal (constant) b Undefined Slope m is undefined (0 in denominator of ratio) b Line is vertical and is NOT a function b Do not say “NO slope”

Linear functions can take on many forms a) Point Slope Form b) Slope Intercept Form c) General (Standard) Form

SLOPE INTERCEPT FORM b Most useful graphing form  To convert from standard to slope intercept, given equation must be solved for y.  To graph, Identify y-intercept (b) and slope (m) Plot y-intercept (this is now your start point) Use rise/run concept to locate other points Draw line through points

y = mx + b Where m = slope of the line and b = y-intercept Examples Examples

POINT-SLOPE FORM b Most useful symbolic form b “Write the equation of the line that meet the following conditions…” b To convert from point-slope to slope intercept, distribute “m” and collect like terms.

y = m(x - x 1 ) + y 1 Where m = slope of the line and (x 1, y 1 ) is any point on the line Examples Examples

SPECIAL LINEAR RELATIONSHIPS b PARALLEL : Two or more lines that run side by side never intersectingnever intersecting always same distance apartalways same distance apart each line has the same slopeeach line has the same slope m 1 = m 2m 1 = m 2

b PERPENDICULAR : Two lines that intersect to form 4 right angles Called “negative reciprocals of each other” (flip and change sign)Called “negative reciprocals of each other” (flip and change sign) Product of the slopes is equal to -1Product of the slopes is equal to -1 m 1 m 2 = -1