Thinking With Mathematical Models Partner Quiz Answers

Test Outline

   * Use a Graph Model to make predictions

• We can draw a line of best fit through the data points
• straight line
• Find Slope (coefficient) for straight lines
• Mark two points find Rise/Run
• Be careful the scale is not always one
• Find the y-intersect
• where the line crosses the y-axis
• If we know the slope and y-intercept we can write the equation
• y=mx+b
• m is slope
• b is the y-intersect
• Click below to see video examples
• Example 1
  
• Example 2
• lines can also be curved

* Explain what Slope and Y-intercept mean based on a problem or situation

• y-intercept is the point where the line crosses the y-line (y-axis).
• Slope is the number that multiplies a variable. It is the ratio of rise/run
• using partner Quiz.

• The slope is 25/1 this means that there are 25 trees planted for every 1 worker.

  The y-intercept is 0. This means that when the number of workers is 0 the number of trees planted is 0 this is the y intercept.

* Write Equations for different situations

    *slope and a point

• Write an equation for the line with slope 2 that passes through the point (4, 12).
• Formula: Y=M•X+B
• Y: (#, # ) Second number in a coordinate pair.
• M: Slope or Rate
• X: ( # , #) First number in a coordinate pair
• B: Y-intercept or initial fee.
• Vocabulary:
• Equation - A mathematical problem (2+2=4)
• Slope - The change in Y over the change in X. Or Rise over Run.
• Point - a pair of variables or a coordinate pair. The make a coordinate on a graph. (#, #)
• Rate - Is the amount variable in an equation change. Same as slope.
• Y-intercept - Is the point where a line passes through the
• To find the y intercept- substitute in y, m, and x
• solve for b.
• 12=2*4+b
• multiply 2*4= 8
• 12=8+b
• subtract 8 from both sides of the equation
• 4=b
• Write your equation
• y=2x+4

    *know a rate and an initial fee

• Your grandfather puts 100 dollars in a savings account for you on your first birthday and then put 10 more dollars into it on each birthday after that.
• initial fee is the starting value, this is your y-intercept (b)
• 100 is the initial fee, b=100
• rate is how much it increases by over time, this is your slope (m).
• 10 is your rate, m=10
• Writing the equation in y=mx+b form
• y=10x+100

    *given two coordinate pairs

    *Find area of a rectangle

    A=l*w

    Area = A, l= length, w=width

* Continue a table

x	0	1	2	3	4	5	6	7	8
y	0	4	8	12	16	20	24	28	32

You continue to add 4 to y and 1 to x. Because the x goes up by 1 and the y goes up by 4.

* Explain if data is linear, or inverse

• Linear
• Graph straight line
• The x and y variables go up by a constant
• Equation Y=mx+b
• Inverse
• Graph Lines that curve
• Table one variable goes up and the other one goes down. When you multiply the variables together it equals a constant
• Equation  x times y=20, x*y= constant

* Write an equation based on a table

Linear

• X	0	2	4	6	8	10	12	14	16
  Y	52	72	92	112	132	152	172	192	212

  
  

• y=mx+b m=slope, b= y-intercept
• When x is 0, The value of y is your y-intercept. In this table our y-intercept is 52.
• To find your Rise and run: What y counts up by is going to be your numerator and what x counts up by is going to be your denominator.
• Rise/run, Rise divided by run= your slope. rise/run= 20/2= 10
• Replace the numbers you know into the equation.
• Slope= 10 m=10
• y=intercept= 52 b=52
• y=10x+52

Inverse

X	1	2	4	5
Y	20	10	5	4

    x*y= constant

    x*y= 20

Practice Problems that you can do to get ready for your test.

(Click to enlarge)

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Thinking With Mathematical Models Partner Quiz Answers

Source: https://sites.google.com/site/msfmath/home/thinking-with-mathematical-models-test-review

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