Unit 6 Lesson 4 Slope Standard AF 3

Unit 6, Lesson 4 Slope Standard: AF 3. 3 Objective: Find the steepness of a line.

SLOPE • Slope is very important to life. • Slopes are everywhere: mountains, rollercoasters, hills, slides, stairs, escalators, ramps, etc. • If the slope is not calculated right, bad things can happen.

Slope • Slope describes the steepness and direction of the line on a coordinate plane. – Always reduce like a fraction or ratio – Keep it improper • Slope = steepness • Example: y = 2 x – The slope is 2 which means the steepness is 2.

SLOPE • Slope is a ratio of RISE OVER RUN for a line. • Remember, ratios can be fractions that compare the same things. RISE RUN

KINDS of SLOPE • There are four kinds of slope. 1) Positive slope 2) Negative slope 3) Zero Slope or No Slope 4) Undefined Slope

Positive Slope = Rise over Run • Positive slope goes uphill • These ratios are always positive

Negative Slope = Rise over Run • Negative slope goes downhill • These ratios are always negative

Zero Slope or No Slope = Rise over Run • These slopes are flat, flat that is why there is no slope. • These slope are always zero

Undefined Slope = Rise over Run • Undefined slope looks like a cliff (vertical line) • These ratios are always 0 on the bottom which is not allowed.

Slope Practice: Identify the type.

How to Find Slope 1) Look at a graph and count RISE over RUN.

Slope from a Graph Slope - The rate of change that determines the direction of a line and how steep it is. vertical change Slope = horizontal change Slope = y x y +2 +3 rise Slope = run +3 3 = Slope = m = +2 2 -6 3 = m= -4 2 -6 x -4

Find the slope of the line below. y rise Slope = run x +4 +1 -2 -8 +1 Slope = +4 1 m= 4 -2 1 = m= 4 -8

Find the slope of the line below. y rise Slope = run -1 +2 x -1 Slope = +2 m= 1 2

Goal 1: Identify from a graph • Identify the type of slope. • Find the slope. Type = M=

Goal 1: Identify from a graph • Identify the type of slope. • Find the slope. Type = M=

Find the slope of the line below. y rise Slope = run -2 +3 x -2 Slope = +3 m= 2 3

Find the slope of the line below. y rise Slope = run +1 +3 x +3 Slope = +1 m=3

Find the slope of the line below. y +4 rise Slope = run +3 x +3 Slope = +4 3 m= 4

Find the slope of the line below. y rise Slope = run x -2 Slope = +1 m = -2 -2 +1

Goal 1: Identify from a graph • Identify the type of slope. • Find the slope. Type: M=

Goal 1: Identify from a graph • Identify the type of slope. • Find the slope. Type = M=

Goal 1: Identify from a graph • Identify the type of slope. • Find the slope. Type = M=

Goal 1: Identify from a graph • Identify the type of slope. • Find the slope. Type = M=