Slopes 8 th Grade Math Presented by Mr. Laws. CCSS Standard 8.F.3 - Interpret the equation y = mx + b as defining a linear function, whose graph is a.

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Presentation transcript:

Slopes 8 th Grade Math Presented by Mr. Laws

CCSS Standard 8.F.3 - Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. 8.F.4 – Find slope: Construct a function to model a linear relationship between two quantities.

Essential Question Using math principles, how do I explain the changes in the y- coordinate (rise)of a graph over the changes of the x – coordinate (run) on a coordinate plane?

Word Definition A slope is the upward or downward slant of a line on a coordinate plane. A rate of change the ratio of the change in y-values to the corresponding change in x-values. A x-axis the positive or negative horizontal number line on a x and y coordinate graph. A y-axis the positive or negative vertical number line on a x and y coordinate graph.

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 x y x Positive Slope Negative Slope upward downward 1. 2.

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

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

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 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) : (1, 2) (3, 5) x 1, y 1 x 2, y 2 Step 1 : Label points Step 2: Substitute points in the slope formula. Step 3 : Find the slope Positive Slope

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

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

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

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