U2D11 Math 8C U2D11 Today We will: Create linear equations from a context and model with tables and graphs.

Must do: Plot the points U2D11 Must do: Plot the points Plot the points A(2, 3) B(-1, -4) C(-3, 3) D(4, -2) C A D B

Plotting Points Write the ordered pair that corresponds to point B. U2D11 Plotting Points Write the ordered pair that corresponds to point B. Now do the same for points A, C, & D (-3,4) (5, 4) (-2, 1) (-4, -3) (1, -2) (3, -4)

Words Worth Knowing Ordered Pair - Any point on the coordinate plane; always in the form of (x,y) Independent Variable - The input of a function, usually denoted x. Always the x-axis when graphing. It does not depend on any other factor in an equation or experiment. Dependent Variable - The output of a function, usually denoted y. Always the y-axis when graphing. It’s value depends on the independent variable.

U2D11 Example There are $500 in Holly’s bank account. Every month she takes $50 out, but does not make any deposits. Make a table of values. Make a graph. Write an equation. Equation: ______________________________

U2D11 Example A rental car company charges an initial fee $50 and then $0.20 for each mile it is driven. 1st, make a table of values and a graph to represent total cost. 2nd, write an equation to represent total cost C, in terms of miles, m Equation: ______________________________________ Miles Cost 200 400

U2D11 You Try! Lin is tracking the progress of her plant’s growth. Today the plant is 5 cm high and she knows that plant will continue to grow 1.5 cm each day. Make a table of values for 0-5 days. Make a graph (don’t forget to label your axes and scale!) Write an equation that represents the plant’s growth per day.

U2D11 Independent Practice U2D11 – ICP Due Today! Also, please get me your requests to reassess ASAP as the term ends in three weeks!

Today We will: Compute Slope U2D12 Math 8C U2D12 Today We will: Compute Slope

Must Do: U2D11 A taxi ride has a flat fee of $3.50 and a charge of $1.50 for every mile travelled. a) Make a table to model this problem b) Make a graph to model c) Make an equation to model d) Using your equation, how far would you go if your cab bill was $48.50?

A taxi ride has a flat fee of $3. 50 and a charge of $1 A taxi ride has a flat fee of $3.50 and a charge of $1.50 for every mile travelled. d) Using your equation, how far would you go if your cab bill was $48.50?

Slope and Linear Equations U2D12 Slope and Linear Equations A linear equation is an equation whose graph is a straight line. Every point on the line is a solution of the equation. These equations can be written in the form where m is the slope of the line, and b is the y-intercept of the line.

Example From yesterday: U2D12 Example From yesterday: The equation that represented Paulina’s bank account savings was What is the slope of the line? What is the y-intercept? What do these values represent for Paulina?

What is slope? Slope is a rate of change. U2D12 What is slope? Slope is a rate of change. Slope is the steepness of a line. How steep is this line?

U2D12 Slope Formula

Find the slope of each line U2D12 Find the slope of each line Slope of line a= Slope of line b= Slope of line c= Slope of line d=

If given only two points on a line… U2D12 If given only two points on a line… We know that slope is So, if given (-2,4) and (4, 12), find the change in y and in x. Slope =

U2D12 Formula! If given two points

U2D12 Example Find the slope of the line crossing through each pair of points: (8, 10), (3, 20) (-2, 4), (9, -7) (6, -2), (6, 11) (5, -1), (1, -1)

Independent Practice U2D12 - ICP

Compare and contract linear functions represented differently. U2D13 Math 8C U2D13 Today We will: Create linear equations from a context and model with tables and graphs. Compare linear equations of the form 𝑦=𝑚𝑥 with equations of the form 𝑦=𝑚𝑥+𝑏. Compare and contract linear functions represented differently.

Must do U2D13 1. Sudzo Wash and Wax charges customers $0.75 per minute to wash a car. Make a table, a graph, and write an equation that relates the total charge C to the amount of time t in minutes. Find the slope of the line that intersects these two points: (-2, -3) and (-10, -4) (0,0) and (-2, -3)

Sudzo Wash and Wax charges customers $0.75 per minute to wash a car.

Practice What does this graph show? U2D13 Practice What does this graph show? Write the equation of the line shown on the graph.

Must Do: Find the slope (2, 1), (3, 6) 4. 5. (-2, -2), (-7, -7) U2D13 Must Do: Find the slope (2, 1), (3, 6) (-2, -2), (-7, -7) (2, 1), (2, -7) 4. 5.

Graphing Linear Equations U2D13 Graphing Linear Equations What do we need to know about a line in order to graph it? Slope A point on the line

U2D13 Equations in Slope-Intercept Form When equations are in Slope-Intercept form, we have the slope and a point! The y-intercept is a point on the y-axis, with ordered pair (0, b)

Equations in Slope-Intercept Form U2D13 Equations in Slope-Intercept Form Where do we start when graphing a line? Example Graph y = 3x + 2 1st plot the y-intercept 2nd use slope to find a second point. 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛 = +3 +1 Last, connect dots to draw the line Slope y-intercept

U2D13 Graph Each Line 𝑦=2𝑥−2 𝑦=−𝑥+1 𝑦= 2 5 𝑥+3 𝑦=− 1 3 𝑥−1

What about these weird ones? U2D13 What about these weird ones? How would you graph something like 𝑦=2? This equation says that y can only ever be 2, regardless of what x is.

U2D13 Graph 𝑦=2

What about these weird ones? How about something like 𝑥=−3? This equation says that x can only ever be -3, no matter what y is.

U2D13 Graph 𝑥=−3

Equations in Slope-Intercept Form U2D13 Equations in Slope-Intercept Form When equations are in Slope-Intercept form, we are given the slope and a point on the y-axis. Example Graph y = 3x + 2 Slope y-intercept

Putting it all together U2D13 Marty is spending money at the average rate of $3 per day. After 14 days he has $68 left. The amount left depends on the number of days that have passed. Identify the variables in this situation: x= _____________ y=_____________ What is the given information in this problem (find all that apply)? y-intercept ________ slope _____ one point ( , ) second point ( , ) What amount of money did he begin with? Write an equation for the situation. Make a graph to represent the problem

Must do: Graph Each Line U2D13 𝑦=3𝑥−1 𝑦=−𝑥 𝑦= 4 5 𝑥−3 𝑦=− 5 2 𝑥+2 x = -4

Must Do: U2D13 A cab company charges a flat fee of $5 plus $0.35 for every mile traveled. The distance traveled is related to the overall fee. Identify the variables in this situation: x= _____________ y=_____________ What is the given information in this problem (find all that apply)? y-intercept ________ slope _____ one point ( , ) second point ( , ) Write an equation for the situation. Make a table and graph to represent the problem. Using your equation, find how many miles you could go for $25.

Must Do: U2D13 1. State the slope and the y-intercept of each line. Then graph the line of each equation: 𝑦=−2𝑥−3 𝑦=−1 Find the slope of the line that crosses between the two points. (-2,5) and (4,-9) (-1,-5) and (-5,-1) Graph the following data and write an equation. Time (sec) 50 55 65 70 80 100 105 120 Distance (mi) 44 46.5 51.5 54 59 69 71.5 79

𝑦=−2𝑥−3 𝑦=−1

Graphing Standard Form Linear Equations Linear Equations Standard Form: Ax+By = C where A, B, and C are numbers Ex. 2x-3y=6 So, how would you graph this?

“Intercept” Method Step #1 – Make an x,y table and fill in zeros 2x-3y=6 Step #2 – Using Standard Form equation, find corresponding x and y values. Step #3 – Plot these points on a graph and draw your line.

Practice: x+y = 2 3x+3y = -1 -x – 2y = 5 x – y = -4

Independent Practice U2D13 – ICP Heads Up!

Construct viable arguments and critique the reasoning of others. U2D14 Math 8C U2D14 Today’s Quiz: Construct viable arguments and critique the reasoning of others. Interpret the results of mathematics in terms of the context in which it was presented. Create linear equations from a context and model with tables and graphs. Compare linear equations of the form 𝑦=𝑚𝑥 with equations of the form 𝑦=𝑚𝑥+𝑏. Compute slope.

Construct viable arguments and critique the reasoning of others. U2D15 Math 8C U2D15 Construct viable arguments and critique the reasoning of others. Interpret the results of mathematics in terms of the context in which it was presented. Create linear equations from a context and model with tables and graphs. Compare linear equations of the form 𝑦=𝑚𝑥 with equations of the form 𝑦=𝑚𝑥+𝑏. Compute slope.

U2D15 The Plan for Today 1st, you will make corrections to your quiz from yesterday and check them off with me. 2nd, you will complete the review packet by the end of the period.

Summative Assessment today:) Standards Assessed: Math 8C U2D16 Summative Assessment today:) Standards Assessed: A. Construct viable arguments and critique the reasoning of others. B. Interpret the results of mathematics in terms of the context. C. Create linear equations from a context and model with tables and graphs. D. Compare linear equations of the form to the form . E. Compute slope.

Math 8C U2D17 Today We will: Determine the equation of a line parallel or perpendicular to a given line.

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