Grab a Unit packet off the Assignment Table and Complete the Bellringer for today in your Unit Packet!

MAFS.8.EE.2.5: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.

Today’s Goals and Agenda By the end of class today I will: I will be able to graph proportional relationships, and compare them, and understand that unit rate is slope. I plan to do this by: ▪ I Do: Introduction to Unit Rate ▪ We Do: Think-Pair-Share Making Money Graphs ▪ I Do: Unit Rate Notes ▪ You Do: Independent Practice (Finish for homework)

Do you remember: Unit Rate from 7 th Grade?

Think back… When you read a problem in your math or science book, is it always written out? Are there other ways to pose a problem without using complete sentences? What might be a way we could display two different relationships, so that we could compare them?

Need to Know: Proportional Relationships can be represented on a graph as a line, so it is a linear relationship and can be written as a linear equation

Making Money Jasmine works as an assistant for lawn care. She was paid $324 for 36 hours. Ben works as a grass-cutter and was paid $248 for 31 hours. Each received a constant rate of pay per hour. Create a graph to represent both scenarios and analyze the graph to determine who made more per hour.

In your Notes or on a Flashcard Write: Slope Slope is the ratio of any two points on a line. It is the constant rate of change of a line All linear relationships have a slope

In your Notes or on a Flashcard Write: How do we calculate Slope? When you have a graph you can use 

You Do: Running and Rising on All Slopes Practice ▪ Don’t forget to title your graph, label the axes, and to have your increments and units marked ▪ When you are finished compare your work with your partner and revise.

Independent Practice-Finish for Homework

Grab the Page of the Unit Packet for today off the Assignment Table and Complete the Bellringer for today in your Unit Packet! Have your homework out on your desk for me to check off.

Slope and Similar Triangles MAFS.8.EE.2.6: Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane

Today’s Goals and Agenda By the end of class today I will: I will be able to explain that slope is a constant rate of change at any point on a line using similar triangles. I plan to do this by: ▪ I Do: Slope Notes ▪ We Do: White Boards Practice Calculating Slope ▪ I Do: Slope Triangles video ▪ We Do: Slope Triangles Practice

Did you read your notes last night? ▪ How can we visually represent proportional relationships? ▪ What is Unit Rate? ▪ What is slope? ▪ How do we calculate slope?

Review ▪ We can display proportional relationships as a line on a graph ▪ Slope is how steep the line on the graph is and is the ratio of the horizontal and vertical change of the line.

▪ A slope is positive If a line rises from left to right (uphill) ▪ A slope is negative If a line falls from left to right (downhill) ▪ If a line is vertical, it has an undefined slope. ▪ If a line is horizontal, it has a slope equal to 0. Write this in your Unit Packet

Write this Down Slope Formula: Using Two Points Example: Find the slope of the line that passes through the points (-2, -2) and (4, 1). ▪ y 2 is the y coordinate of the 2 nd ordered pair (y 2 = 1) ▪ y 1 is the y coordinate of the 1 st ordered pair (y 1 = -2)

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

Write this Down Slope Formula: Rise over Run Start with the lower point and count how much you rise and run to get to the other point! 6 3 run 3 6 == rise

Use Rise over Run to solve for Slope

Find the Slope x y x y slope = Use Rise over Run to solve for Slope

How can we prove that slope is constant at any two points on the graph? ▪ We can use similar triangles! ▪ What do you remember about similar triangles? – Corresponding sides are proportional, Slope is a proportion! ▪ Understanding Similar Triangles and Slope Video: math-ee-vidslopeline/slope-similar-triangles/ math-ee-vidslopeline/slope-similar-triangles/

Do Now Pull out your notes on slope, your slope workbook pages from the substitutes, and your Bellringer from Friday. I am checking them- if they are not out by the time the bell rings I am deducting 10 points.

Slope Review and Deriving Slope-Intercept Form MAFS.8.EE.2.6: Derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

Today’s Goals and Agenda By the end of class today I will: I will be able to interpret slope in multiple ways and derive slope-intercept form. I plan to do this by: ▪ We Do: Game of Slopes Class Competition ▪ I Do: Slope-Intercept form Notes ▪ We Do: Game of Slopes Part 2

Maria put 3 tablespoons of powdered cocoa in 8 ounces of milk. Brandon put 12 tablespoons of powdered cocoa in 36 ounces of milk. Is this a proportional relationship?

A tub that holds 18 liters of water fills with 2 liters of water every 2.5 minutes. Create a graph that models the situation for the first 5 minutes. At what rate is the tub filling with water?

Which of the pairs of triangles can be used to slope is the same at any point on the line A B C D

Find the Slope of the Table Below and then find the next point of the line

Find the Slope

DO NOW: On a blank sheet of paper, write down in a few sentences how you think you would approach solving this. Then find the slope of the table. If you finish early pull out your unit packet and unpack standard MAFS.8.EE.2.6

Deriving Slope-Intercept Form MAFS.8.EE.2.6: Derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

Today’s Goals and Agenda By the end of class today I will: I will be able to interpret slope in multiple ways and derive slope-intercept form. I plan to do this by: ▪ I Do: Slope-Intercept form Notes ▪ We Do: Slope Form White Board Practice ▪ You Do: Exit Ticket Quiz ▪ Linear Equations Project Directions

Important!: Write this Down y = mx + b and y=mx m represents the slope b represents the y-intercept Example: y = 5x + 3 The slope is 5 and the y-intercept is 3 Slope Intercept Form

Important!: Write this Down Where a straight line crosses an axis of a graph. Intercept(s)

What are the x- and y-intercepts? The x-intercept is where the graph crosses the x- axis. The y-coordinate is always 0. The y-intercept is where the graph crosses the y- axis. The x-coordinate is always 0. (2, 0) (0, 6)

3x – 4y = 24? What is the x-intercept of 3x – 4y = 24? 1.(3, 0) 2.(8, 0) 3.(0, -4) 4.(0, -6)

-x + 2y = 8? What is the y-intercept of -x + 2y = 8? 1.(-1, 0) 2.(-8, 0) 3.(0, 2) 4.(0, 4)

Find the slope and y-intercept of y = -2x m = 2; b = 4 2.m = 4; b = 2 3.m = -2; b = 4 4.m = 4; b = -2

Let’s Try this Again

Pull out a Sheet of Paper Exit Ticket- Pop Quiz You may use your notes No talking Write the problem, show your work and make your answers clear.

Which of the pairs of triangles can be used to slope is the same at any point on the line A B C D

Find the Slope of the Table Below and then find the next point of the line

Find the Slope

Find the slope and y-intercept of y = -2x + 4

Write the equation of a line that has a y-intercept of -3 and a slope of -4.

Writing Equations MAFS.8.EE.2.6: Derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

Today’s Goals and Agenda By the end of class today I will: I will be able to write equations in Slope Intercept Form and in Standard Form I plan to do this by: ▪ I Do: Writing Equations Notes ▪ We Do: White Board Practice ▪ You Do:

Writing Equations When asked to write an equation, you need to know two things : slope (m) y-intercept (b)

Writing Equations – Type #1 Slope and y-intercept Given Write an equation in slope-intercept form of the line that has a slope of 2 and a y-intercept of 6. ▪ To write an equation, you need two things: slope (m) = y – intercept (b) = ▪ We have both!! Plug them into slope-intercept form: y = mx + b y=2x+6

Write the equation of a line that has a y-intercept of -3 and a slope of y = -3x – 4 2.y = -4x – 3 3.y = -3x y = -4x + 3

Writing Equations – Type #2 Slope and an Ordered Pair Give ▪ Write an equation of the line that has a slope of 3 and goes through the point (2,1). ▪ To write an equation, you need two things: ▪ slope (m) = ▪ y – intercept (b) = ▪ We need to solve for the y-intercept!! Plug in the slope and ordered pair into y = mx + b 1 = 3(2) + b

Writing Equations – Type #3 Two Ordered Pairs Given Write an equation of the line that goes through the points (-2, 1) and (4, 2). To write an equation, you need two things: slope (m) = y – intercept (b) = We need both!! First, we have to find the slope. Plug the points into the slope formula and simplify.

Write an equation of the line that goes through the points (0, 1) and (1, 4). 1.y = 3x y = 3x y = -3x y = -3x + 1

Ax + By = C where A, B, and C are integers Example: x + 3y = 6 Standard Form Important!: Write this Down

-3 Find the slope and y-intercept. 5x - 3y = 6 Write it in slope-intercept form- Solve for y! (y = mx + b) 5x – 3y = 6 -3y = -5x + 6 y = x - 2 m = b = -2

Write it in slope-intercept form. (y = mx + b) 2y + 2 = 4x 2y = 4x – 2 y = 2x - 1 Find the slope and y-intercept. 2y + 2 = 4x 222 m = 2 b = -1

Oh no! This is a Type #3 problem! Find slope… Find y-intercept by solving for y. I’m choosing the point (-4, 6). 6 = -3(-4) + b 6 = 12 + b -6 = b Slope-intercept form: y = -3x - 6 Standard form: 3x + y = -6 Write the standard form for a line passing through the points (-1, -3) and (-4, 6).

Graphing Linear Equations MAFS.8.F.2.4 (DOK 3): Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

By the end of today, you will be able to… graph a line given any linear equation.

We have used 3 different methods for graphing equations. 1)using a t-table 2)using slope-intercept form 3)using x- and y-intercepts The goal is to determine which method is the easiest to use for each problem!

Here’s your cheat sheet! If the equation is in STANDARD FORM (Ax + By = C), graph using the intercepts. If the equation is in SLOPE-INTERCEPT FORM (y = mx + b), graph using slope and intercept OR a t-table (whichever is easier for you). If the equation is in neither form, rewrite the equation in the form you like the best!

Graph Which graphing method is easiest? Using slope and y-intercept (or t-table)! These notes will graph using m and b m =, b = 2

Graphing with slope-intercept 1.Start by graphing the y-intercept (b = 2). 2.From the y-intercept, apply “rise over run” using your slope. rise = 1, run = -3 3.Repeat this again from your new point. 4.Draw a line through your points. (1) (-3) Start here (1) (-3)

Graph -2x + 3y = 12 Which graphing method is easiest? Using x- and y-intercepts! (The equation is in standard form) Remember, plug in 0 to find the intercepts.

Review: Graphing with intercepts: -2x + 3y = 12 1.Find your x-intercept: Let y = 0 -2x + 3(0) = 12 x = -6; (-6, 0) 2.Find your y-intercept: Let x = 0 -2(0) + 3y = 12 y = 4; (0, 4) 3.Graph both points and draw a line through them.

Which method is easiest to graph -3x + 6y = 2? 1.T-table 2.Slope and intercept 3.X- and Y-intercepts 4.Graphing calculator

Which is the graph of y = x + 2?