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Transcript of Window 12
I took the one less traveled by,
And that has made all the difference."
- Robert Frost (BACK OF FOLDABLE)
Window 12 Standards 8.3.8: Understanding the relationships among tables, equations, verbal expressions, and graphs of linear functions.
8.3.1: Write and solve linear equations and inequalities in one variable (yes, we just did this one...we are doing it again) Flap 1 COVER:
We can use tables to measure rate of change
We use data from the tables to write a linear equation
We put all of this together to draw a graph
We use our linear equation to write a verbal expression
INSIDE FLAP 1
How To Steps - Writing a Linear Equation from a Table
REMEMBER - THE LEFT COLUMN IS X!! Step 2: Look at the data table and determine how x and y values are changing
REMEMBER - THE LEFT COLUMN IS X
ie: how the numbers are going up or down Step 3: Once you determine how x and y are changing, place the y value over the x value in a fraction. This is your SLOPE or m value in y=mx+b Step 1: Look at the data table and find the coordinate pair that has a 0 value for x. The y value is the y-intercept or b in y=mx+b t d
3 13 (INSIDE FLAP 1)
EXAMPLE Look at the table below and draw it in your foldable. Using our "how-to" steps...
1) Find the y-intercept by looking for the ordered pair that has an x value of 0. b=____
2) Determine the rate of change for both the x and y values. How much do x and y go up each time? x=____ y=_____ 3) Put the y change over the x change in a fraction. This is slope. m = ______
4) Write your linear equation
y = ____ x + _____ (INSIDE FLAP 1)
How To Steps: Plotting the graph of a line from a linear equation Step 1: Plot the y-intercept. On the y-axis, put a "dot" on the y-intercept value.
Step 2: Use the rise over run to plot two more points. Starting from the y-intercept dot, count the rise. Then, count the run. Put another "dot" on that point.
Step 3: Starting from the new dot, repeat Step 2.
Step 4: Draw a straight line through your points. Plot the line from our example. (Flap 1 INSIDE) As a verbal expression... As x increases by 1, y increases by 4. Flap 2 COVER:
1) VARIABLE: A symbol for a number we don't know yet. It is usually a letter like x or y but it can be any letter
2) Single Variable: only one letter in the equation
3) Algebraic Expression: a mathematical phrase that can contain ordinary numbers, variables (like x or y) and operators (like add,subtract,multiply, and divide) (Flap 2 INSIDE) How to Steps...solving single variable algebraic expressions 1) Addition...
For x + 1=2 or 1 + x=2, subtract 1 on each side.
For x-1=2, add 1 on each side
For 1-x=2: TWO STEPS! Subtract 1 on each side. You are left with -x = 1 (THE MINUS SIGN DOESN'T GO AWAY!) Then, divide by the "invisible" -1 on each side. How to Steps...solving single variable algebraic expressions (FLAP 2 INSIDE) 3) Multiplication
For 3x = 12. A number next to a letter means that something is being multiplied. To solve for the letter, do the opposite of multiplying which is dividing How to Steps...solving single variable algebraic expressions FLAP 2 (INSIDE) 4. Division
For x/3 = 12. When we see a fraction bar, we know that something is being divided. To solve for the letter, do the opposite of dividing which is multiplying by 3 on each side. For 44/x = 4. When the variable is in the denominator, we must do two steps. First, multiply each side by the variable. On the left side, the variable cancels out. On the right, we have 4x. Our new equation is: 4x=44. Solve this as a multiplication variable problem. Example Problems
1) c + 3/10 = 1/5 2) 5/6y = 3/4
3) x/1.2 = -6 A Word From Mrs. Hogan... This is our last foldable. Thank you for your participating in math class. I wish you all the very best life has to offer.
May your summer be filled with sunny beaches, your nights filled with starry skies, your days filled with laughter, and your hearts filled with joy, now and always.
Best of Luck, Class of 2017!