1. Lesson 4.2 Review of 4.1 E.Q. #1 E.Q. #2
Given a y-intercept & a slope can you write the equation of the line?
slope: 2
Y-intercept: 9
 y = 2x + 9
 f(x) = 2x + 9
E.Q. #2
Given the graph of a linear function, how can you write the equation of the line?

2. Review of 4.1 (continued) E.Q. #3 E.Q. #4
Given two points can can you write the equation of the line?
E.Q. #4
Given real-life problem, how do you model using mathematics the equation of the line?
Linear Model – a linear function that models a real-life situation

3. Given a slope (m) and a point on a graph: 1 – Find the y-intercept
2 – Sketch the line
3 – Write an equation and a function of the line
m= ½
Find the y-intercept. – use the point you have to create the equation.
Use (3, 2)
y = mx + b
2 = 1/2(3) + b
Solve for b  2= 3/2 + b  2 – 3/2 = b  b = ½
Plot the y-intercept
Draw the linear equation
Write the equation & function
y = ½ x + ½ or f(x) = ½ x + ½
Is there another way to do this?

4. Objective: Writing equations of a line in Point – Slope Form
Vocabulary
Point – Slope Form is a linear equation written in the form
(y – y1) = m (x – x1)
The line of the equation passes through the point (x1 , y1) and the slope of the line is m
Essential
Question #1:
What is the origin on the point – slope form?
Passing through (x1 , y1) m=
(y2 – y1)
(x2 – x1)
Multiply both sides by (x2 - x1)
m(x2 – x1) = (y2 – y1)
Slope

5. Essential Question #2: Essential Question #3:
How do you write an equation using a slope and a point?
Point: ( - 8, 3)  (x1 , y1)
Slope (m): ¼
(y2 – 3) = ¼ (x2 + 8 )
Essential
Question #3:
How do you write an equation using two points? m=
(y2 – y1)
(x2 – x1)
Step 1: Find the slope of the line
Step 2: Use the lope and one set of ordered pairs to write the equation of the line.
(x1 , y1)
(y2 – y1) = m(x2 – x1)
Slope

6. Using the other ordered pair:
Example 1:
Find the slope and write the equation
Ordered pairs: ( 1 , 2 ) & ( 3, - 2 ) m=
(y2 – y1)
(x2 – x1) m=
( –2 – 2 )
(3 – 1)
(m)= - 2
(y2 – y1) = m(x2 – x1)
(y2 – 2) = -2(x2 – 1)
Distribute:
y - 2 = - 2x + 2
Solve for y:
y = - 2x + 4
Using the other ordered pair:
(y2 + 2) = -2(x2 – 3)
Distribute:
y + 2 = - 2x + 6
Solve for y:
y = - 2x + 4

7. Using the other ordered pair:
Example 2:
Find the slope and write the equation
Ordered pairs: f(4) = (-2) & f(8) = ( 4 )
or ( 4 , -2 ) & ( 8 , 4 ) m=
(y2 – y1)
(x2 – x1) m=
(4 – -2 )
(8 – 4) m=
(6)
(4)
(m)= 3/2
(y2 – y1) = m(x2 – x1)
(y2 + 2) = 3/2 (x2 – 4)
Distribute:
y + 2 = 3/2 x - 6
Solve for y:
y = 3/2 x - 8
Using the other ordered pair:
(y2 - 4) = 3/2 (x2 – 8)
Distribute:
y - 4 = 3/2 x - 12
Solve for y:
y = - ½ x - 8

8. Example 3: Find the slope and write the equation of a linear model
The student council is ordering customized foam hands to promote school spirit. The table shows the cost of ordering different numbers of foam hands. Can the situation be modeled by a linear equation? If possible, write a linear model that represents the cost as a function of the number of foam hands.
m= = 24/4
(82 – 58 )
(12 – 8)
m= = 24/4
(70 – 46 )
(10 – 6)
m= = 24/4
(58 – 34 )
(8 – 4)
(m)= 6
(y2 – y1) = m(x2 – x1)
(y ) = 6 (x2 – 8)
Distribute:
y = 6 x - 48
Solve for y:
y = 6 x + 10

9. Objective: Writing equations of a line in Point – Slope Form
Have we answered all the essential questions?
What is the origin on the point – slope form?
How do you write an equation using a slope and a point?
How do you write an equation using two points?
Have we achieved our Objective?
Objective: Writing equations of a line in Point – Slope Form
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