Warm-up #32 (Thursday, 12/3/2015) Find the slope of (5, -4) and (-3, -2) y + 5 = 4x, solve for y 3x – y = 3, solve for y

Homework Thursday, 12/3 Lesson 4.02 packet Page 2

Lesson 4.02 Point-Slope Form

What is Slope? Steepness Rise Run Amount of Slant y=mx + b +SLOPE + Change in Y Change in X - SLOPE - Rise Run Amount of Slant y=mx + b

Slope Summary Positive Slope Slope = 0 Undefined Slope Negative Slope Cross country skiing Up the ski lift Slope = 0 Positive Slope Undefined Slope Down the slopes Oops! Negative Slope

Slope Slope: a number that describes both the direction and the steepness of the line. Slope can be positive, negative, zero, or undefined. You can find slope using 2 points. Theorem 4.1: The slope between any 2 points on a line is constant

The slope of a line is a number, m, which measures its steepness. y x 2 -2 m is undefined m = 2 m = 1 2 m = 0 m = - 1 4

Objective The student will be able to: find the slope of a line given 2 points and a graph. SOL: A.6a Designed by Skip Tyler, Varina HS and Vicki Hiner, Godwin HS

What is the meaning of this sign? Icy Road Ahead Steep Road Ahead Curvy Road Ahead Trucks Entering Highway Ahead

Slope can be expressed different ways: A line has a positive slope if it is going uphill from left to right. A line has a negative slope if it is going downhill from left to right.

1) Determine the slope of the line. When given the graph, it is easier to apply “rise over run”.

Determine the slope of the line. Start with the lower point and count how much you rise and run to get to the other point! rise 3 = = run 6 6 3 Notice the slope is positive AND the line increases!

2) Find the slope of the line that passes through the points (-2, -2) and (4, 1). When given points, it is easier to use the formula! y2 is the y coordinate of the 2nd ordered pair (y2 = 1) y1 is the y coordinate of the 1st ordered pair (y1 = -2)

You can do the problems either way! Which one do you think is easiest? Did you notice that Example #1 and Example #2 were the same problem written differently? 6 3 (-2, -2) and (4, 1) You can do the problems either way! Which one do you think is easiest?

3) Find the slope of the line that goes through the points (-5, 3) and (2, 1).

Determine the slope of the line shown. -2 -½ ½ 2

Determine the slope of the line. -1 Find points on the graph. Use two of them and apply rise over run. 2 The line is decreasing (slope is negative).

What is the slope of a horizontal line? The line doesn’t rise! All horizontal lines have a slope of 0.

What is the slope of a vertical line? The line doesn’t run! All vertical lines have an undefined slope.

Slope is sometimes referred to as the “rate of change” between 2 points.

used to represent slope. The letter “m” is used to represent slope. Why?

If given 2 points on a line, you may find the slope using the formula m = y2 – y1 x2 – x1

The formula may sometimes be written as m =∆y . ∆x What is ∆ ?

Find the slope of the line through the points (3,7) and (5, 19). x1 y1 m = 19 – 7 5 – 3 m = 12 2 m = 6

(3, 4) and (-6, -2) m = -2 – 4 -6 – 3 m = -6 -9 m = ⅔

What if the numerator is 0? denominator is 0?

If given an equation of a line, there are 2 ways to find the slope and y-intercept.

One method is to write the equation in slope-intercept form, which is y = mx + b. slope y-intercept

y = 3x + ½ Find the slope and y-intercept of the following equations.

First, solve the equation for y. 3x + 5y = 10 First, solve the equation for y. 3x + 5y = 10 5y = -3x + 10 y = -3/5 x + 2 m= -3/5 b = 2

If given the graph of a line, find the slope by using the “triangle” method to find the rise over run.

rise = 4 m= rise run run = 5 m= 4/5

Objectives To learn what slope is To learn what a line looks like when it has positive, negative, zero or undefined slope To learn how to find the slope of a graph To learn how to find the slope given 2 points To learn how to find the slope of a table

What is Slope? Slope is the rate of change of a line (change in y) (change in x)

What does the line look like when… You have positive slope? You have negative slope? You have zero slope? You have NO slope?

Slope Mountain Ski Resort T. Merrill 2005 Positive slope, + work Negative slope, - work Zero slope is zero fun! NO slope. Oh No!!!! Slope Mountain Ski Resort T. Merrill 2005

Lets Cheer Positive, Negative Zero NO X-Axis Y-Axis Go, Go, Go

What Type of Slope is Shown? Positive Slope Negative Slope Zero Slope No Slope/Undefined

Slope of a Graph When slope is positive or negative we need to find the actual value of the slope or rate of change On a graph we find slope using the formula How far up or down it changes How far left or right it changes

Slope of a Graph First pick two points on the line The points need to be where the lines cross so they are integers 2. Then find the rise and run 3. Determine if the slope of the line is positive or negative Rise = 2 Run = 3

Slope of a Graph First pick two points on the line The points need to be where the lines cross so they are integers 2. Then find the rise and run 3. Determine if the slope of the line is positive or negative Rise = 10 Run = 2

Slope of a Graphed Line Find the slope of each line below x y Slopes: Find the slope of each line below 4 4

Slope of line through 2 points To find the slope of a line through 2 given points we use the formula For example, Find the slope of a line that goes through (-3, 5) and (2, 18) -3 5 18 2 X1 y1 X2 y2

Given two points on a line, find the slope: 1. (9, 2), (8, -7) X1 y1 X2 y2 2. (-4, 4), (-7, 2) y1 X2 X1 y2 3. (5, -1), (9, -4) X1 y1 y2 X2

Given two points on a line, find the slope: 4. (5, 2), (1, 0) X1 y1 X2 y2 5. (3, -3), (3, -1) y1 X2 X1 y2 Undefined, NO slope 6. (-4, -2), (4, -2) X1 y1 y2 X2

If it is linear it will be the same no matter which two rows you pick Slope of a Table In a table we can use the same formula. Pick any two pairs in the table for coordinates Pick any two rows. If it is linear it will be the same no matter which two rows you pick x y -4 -17 1 -2 3 4 8 19 10 25 x1 y1 x2 y2

Slope of a Table Find the slope for each table below x y -3 4.25 -1 2.75 2 1 1.25 5 -1.75 x y -8 2 -6 3 -3 4.5 -1 5.5 6

Slope of a Table Find the slope for each table below x y -10 17 -5 10 4.4 5 -4 -11 x y -3 -8 -1 1 4

Conclusion Slope is: Describe the slope of each of the following the rate of change of a line Undefined/ No slope Positive slope Negative slope Zero/0 slope