unit 4b day 3
DESCRIPTION
Unit 4B Day 3. Point-Slope. Warm-Up #3 . HW Check . Core Time. Writing equations of lines. Use slope-intercept form if you are given: The slope and the y-intercept Two ordered pairs (one of which is the y-intercept) Word Problems that have rates flat fees/one-time payments - PowerPoint PPT PresentationTRANSCRIPT
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Unit 4B Day 3Point-Slope
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Warm-Up #3
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HW Check
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Core Time
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Writing equations of linesUse slope-intercept form if you are given:
a) The slope and the y-interceptb) Two ordered pairs (one of which is the y-
intercept)c) Word Problems that have rates flat fees/one-
time payments
Use Standard form with WORD PROBLEMS only!! -- With two items that add up to a total
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If you are given a) The slope and a point (not the y-intercept)
b) Two ordered pairs (neither the y-intercept)
Use the point-slope formula!!!
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Point – Slope FormulaIf you know one point a line passes through and
the slope of the line.
Point Slope Formula:
m = Slope is the ordered pair
Y and x stay as the variable y and x * Never plug in for them!
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Ex.1 A line passes through the point (3, 4) and has a slope of 2. Write the equation of the line:
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2. Write the equation of the line that has a slope of -3 and passes through the point (-1,7).
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Converting to Slope-Intercept
Step1: DistributeStep2: Move the constanton the left to the right.
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3.
Change to Slope-intercept Form
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Ex. 4 Ex. 5
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6. Write the equation of the line that has a slope of and passes through the point (5, -7).
Make sure your final answer is in slope-intercept form.
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a)Write an Equation of the line with: b) Change to Slope-intercept form
7. (-1, -3); Slope = 4y + 3 = 4(x + 1)
8. (-10, 0); Slope = 2y = 2(x +10)
9. (-4, 3); Slope = -6y – 3 = -6(x +4)
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10. (-3, 6) and (1, -2)y – 6 = -2(x + 3) or y + 2 = -2(x –
1)11. (-2, 3) and (-1, 1)
y – 3 = -2(x + 2) or y – 1 = -2(x + 1)
12. (-2, -5) and (7, -6)y + 5 = - (x + 2) or y + 6 = - (x –
7)
a) Write an Equation in Point-Slope Form Given Two Pointsb) Change to slope intercept form
91
91
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Writing an Equation from a Table
What is the independent and dependent variable?x – independent; y – dependent
Find the rate of change:
What is the slope?4/10 = 2/5
What is one ordered pair?(-11, -7), (-1, -3), (4, -1), (19, 5)
What is a possible equation in Point-Slope Form?y + 7 = 2/5 (x + 11)
tindependenin changedependentin change change of rate
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Example:Altitude Temp.8000 197.64500 203.93000 206.62500 207.5
Boiling Point of Water
Is the relationship shown by the data in the table linear? If so, model the data with an equation.
Step 1: Find the rates of change for each ordered pair.
Step 2: Use the slope and a point to write an equation.
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Step 1: Graph the ordered pair.Step 2: Starting at the ordered pair, use yourslope to graph anotherpoint on the line.
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Write the equation of the line in Point Slope Form
Step 1: Find the slope Using the two points
Step 2: Pick one of the Points.
Step 3: Use step 1 and Step 2 to substitute into The point slope formula
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SummarySlope - Int.
FormStandard Form Point - Slope Form
y = mx + b Ax + By = C y – y1 = m(x - x1)x and y are variables
x and y are variables
x and y are variables
m = slopeb = y-int.
A, B and C are WHOLE Integers
(x1 y1) is a point on the equation or
graph
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HW: 4.4
Complete the worksheet on Standard form