Warm-Up1. What is the slope & y-intercept of the line

2x – 5y = 10?

2. Find the slope between the points (-15, -3) and (6, 4)

3. Write the equation of the line in slope-intercept form.

HW Check 4B.2

21. 4x - y = 11

22. 2x - y = 6

23. 2x + y = -3

25. 2x - 3y = 25

27. 4x + 5y = 6

28. x + 5y = 0

29. 5x - 2y = 44

33. 5x + 10y = 20034. 5x + 3y = 450 35. 5x + 7y = 70

Standard Form

Only write equations in standard form if you are given a word problem. Only write a word problem in standard form if you

are NOT given a rate and a flat fee. Standard form word problems can only be written

if you have two unknowns that add up to a total. DO NOT write an equation in standard form if

you are given the slope and y-intercept. That equation should be written in

_____________ form.

Quick Review

1. What is the Slope-Intercept Form?

y = mx + b

2. What is the Standard Form?

Ax + By = C

3. How does an equation of a vertical line look? What is the slope?

x = #, slope = undefined

4. How does an equation of a horizontal line look? What is the slope?

y = #, slope = 0

Point-Slope Form

y – y1 = m(x – x1)

m = slope

(x1,y1) = a point that the line goes through

Best used when:

When you are given the slope and a point (that is not the y-intercept) and you need to write the equation of the line.

Point – Slope Form

y – y1 = m(x - x1)

y – coordinate x – coordinate

Goes through point (5, 6) and has slope of 3

Example: y – 6 = 3(x – 5)

SLOPE

Write the equation in point-slope form that

Point-Slope Form

(x, y)

1. Write the equation in Point-Slope Form of the graph below if it goes through the point (-5,-4) and has a slope of 2/3:

11 xxmyy

Write an Equation in Point-Slope Form Given a Point and a Slope

2. (-1, -3); Slope = 4

y + 3 = 4(x + 1)

3. (-10, 0); Slope = 2

y = 2(x +10)

4. (-4, 3); Slope = -6

y – 3 = -6(x +4)

11 xxmyy

Steps:

1. Find the slope between the two points.

2. Pick one point to use in order to write the equation.

3. Plug in the slope and coordinate from the point into the Point-Slope Form

Write an Equation in Point-Slope Form Given Two Points

5. (-3, 6) and (1, -2)

y – 6 = -2(x + 3) or y + 2 = -2(x – 1)

6. (-2, 3) and (-1, 1)

y – 3 = -2(x + 2) or y – 1 = -2(x + 1)

7. (-2, -5) and (7, -6)

y + 5 = - (x + 2) or y + 6 = - (x – 7)

Write an Equation in Point-Slope Form Given Two Points

9

1

11 xxmyy

9

1

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 change

dependentin change change of rate

Example:

Altitude Temp.

8000 197.6

4500 203.9

3000 206.6

2500 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.

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 of the equation or

graph

Wrap Up

Point-Slope Form Graph Using Point-Slope form

Start at the point Graph the slope

Write equation in point-slope form Given a point and a slope Given two points

Writing an equation from a table Find the rate of change (slope) Pick a point to plug in

What two things are given to you in the point-slope form?

11 xxmyy