Welcome to Unit 8: LINEAR Functions

Introduction to Slopes

Slopes in Real Life

What is the slope of a line? Rate of change Rise/Run Steepness of a line Change in Y/Change in X

Ways to solve for SLOPE 1) Graphs 2) Tables 3) Points 4) Equations

Finding slope using a graph Rise is -1 Run is 2 −1 2

Example: Finding slope using a graph

Volunteer?

Find the slope of the line that passes through two given points. Example: R(1,2), S(-4,3) Hint: Use the slope formula.

Find the slope of the line that passes through two given points. Given: A(4,6), B(3,8) Hint: Use the slope formula.

Volunteer? Given: C(6,-2), D(10,4)

Slope Formula: Using a table to find the slope X Y 1 12 3 9 5 6 7 𝐶ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑌 𝐶ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑋 = Slope 9−12 3−1 = −3 2 =− 3 2

Slope Formula: Using a table to find the slope X Y 2 1 4 6 3 8 10 5

Volunteer? X Y -3 -2 -9 -15 -21 -27

Try This One… The slope of a line that goes through the points (r, 6) and (4, 2) is 4. Find r.

To solve this, plug the given information into the formula The slope of a line that goes through the points (r, 6) and (4, 2) is 4. Find r. To solve this, plug the given information into the formula

To solve for r, simplify and write as a proportion. Cross multiply. 1(-4) = 4(4 – r)

Simplify and solve the equation. 1(-4) = 4(4 – r) The ordered pairs are (5, 6) and (4, 2)

SLOPE DUDE http://www.teachertube.com/video/slope-dude-125151

Slope To determine if slope is positive or negative, look at the line from left to right (just like you read). Down …negative. UP…positive.

Formula for Slope A way to remember which value goes on top. 2 Y 1 -Y m = 2 X 1 - X Keep the pairs together.

y horizontal line = any number What does an upside-down h look like? Is always a horizontal line. Zero slope

x Vertical line = any number What does an upside-down and right-side up V look like? = any number Is always a vertical line. x Undefined slope