Unit 4B Day 3Point-Slope

Warm-Up #3

HW Check

Core Time

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

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!!!

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!

Ex.1 A line passes through the point (3, 4) and has a slope of 2. Write the equation of the line:

2. Write the equation of the line that has a slope of -3 and passes through the point (-1,7).

Converting to Slope-Intercept

Step1: DistributeStep2: Move the constanton the left to the right.

3.

Change to Slope-intercept Form

Ex. 4 Ex. 5

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.

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)

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

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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

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.

Step 1: Graph the ordered pair.Step 2: Starting at the ordered pair, use yourslope to graph anotherpoint on the line.

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

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

HW: 4.4

Complete the worksheet on Standard form