Slopes and Rate of Change Math I Presented

Slopes and Rate of Change Math I Presented by Mr. Laws

Standards • F. IF. 6 – Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

Essential Question • Using math principles, calculate and interpret the average rate of change of a linear function?

Target Statement • I CAN find and interpret the rate of change and slope of lines.

What is a slope? •

4 Types of Slopes • There are four types of slopes on a coordinate plane. • Always read slopes from left to right on a coordinate plane. y y up wa x d ar nw Positive Slope w rd 2. do 1. Negative Slope x

4 Types of Slopes y y 4. Horizontal Zero Slope x vertical 3. Undefined Slope x

Rise over Run • Slope (m) can also be represented as rise (y) over run (x). • Rise is the vertical change in a line. (Up or down) • Run is the horizontal change in the line. ( to the right). Slope Model:

Rise over Run

Rise over Run

Rules for Finding Slope • Always reduce slopes to its lowest term like a fraction. • The rise can be positive or negative; the run is only positive. • If the run is negative, move it to the rise to make the slope negative. • If the rise and run is negative, change the slope to positive.

Slope Formula is used to help you find the slope of a line between two points. Slope Formula: (x 1, y 1) (x 2, y 2)

Finding the Slope w/Slope Formula Example 1: Find the slope between (1, 2) and (3, 5) : x 1, y 1 x 2, y 2 (1, 2) (3, 5) Step 1 : Label points Step 2: Substitute points in the slope formula. Positive Slope Step 3 : Find the slope

Finding the Slope w/Slope Formula Example 2: Find the slope between (-1, 3) and (3, -2) : x 1, y 1 x 2, y 2 (-1, 3) (3, -2) Remember: when subtracting a negative number, change to positive! Negative Slope

Finding the Slope w/ Slope Formula Example 3: Find the slope between (2, 3) and (5, 3) : x 1, y 1 x 2, y 2 (2, 3) 5, 3) Zero Slope

Finding the Slope w/ Slope Formula Example 4 : Find the slope between (4, -2) and 4, 3) : x 1, y 1 x 2, y 2 (4, -2) (4, 3) Remember: when subtracting a negative number, change to positive! Undefined Slope

Summary • Can you answer the essential question? • Can you complete the target question. • Do you have any questions on what you have learned? • Will you be able to write a summary based on the lesson?