Warm–up #11. Find midpoint between (a, b) & (b, a)2. Find midpoint between (, 0) & (3, 0)

Warm–up #1 Solutions1. Find midpoint between (a, b) & (b, a) (x1, y1) (x2, y2)

Midpoint =

=

Warm–up #1 Solutions2. Find midpoint between (, 0) & (3, 0) (x1, y1) (x2, y2)

Midpoint =

=

=

= (, 0)

Homework LogThurs

10/29

Lesson 3 – 1

Learning Objective: To find slope & graph equations

Hw: #302 Pg. 168 #31 – 63 odd

10/29/15 Lesson 3 – 1 Graphing Linear Equations Day 2

Advanced Math/Trig

Learning Objective To find slope of a line given an

equation

To find missing coordinate given slope

To find missing coordinate of collinear points

To determine whether four given points are vertices of a parallelogram

To sketch a graph of equations

Given Ax + By = C, find slope

Given: Ax + By = CThen slope

1. Find slope 4x – 2y = 20

A = 4 B = –2

Or get into y = mx + b

4x – 2y = 20–4x –4x–2y = –4x + 20–2 –2 –2y = 2x – 10

Find slope 2. x – 7 = 0

Since no y, just solve for x

x = 7

Vertical line

Slope is undefined

3. y = –2

Horizontal line

Slope = 0

Applying Midpoint4. Midpoint: (–2, 7), one endpoint: (3, –5), find other endpoint (.

Midpoint =

(–2, 7) =

–2 = 7 =

–4 = 3 + 14 = –5 +

(

Set each coordinate

part = to each other

(

Applying Slope5. Suppose 3 points (1, –1), (–2, 8), and (x, –7) lie on a straight line. Find the missing coordinate.

Find slope = =

Use slope and other set of points to solve

= =

–3(x+2) = 1(–15)

–3x – 6 = –15

–3x = –9 x = 3

Make a table and plug values into y and

solve for xy

x

Sketch the graph

│–2│–1

│–1│ – 1

│0│ – 1

│1│ –1

│2│ – 1

–2

–1

0

1

2

1

0

–1

0

1

x │y│ – 1 y

6.

y

x

Sketch the graph

Plug values into y & solve

for x

–2

–1

0

1

2

yy2 + 1x

(–2)2 + 1

(–1)2 + 1

(0)2 + 1

(1)2 + 1

(2)2 + 1

5

2

1

2

5

7.

ParallelogramTo determine vertices of Parallelogram:

• Sketch a graph

• Show Opp. Sides are parallel → same slope

Determine whether the four

given points are vertices of a

parallelogram.

8. (–1, 1), (–2, –1), (1, –4), (0, –6)

DON’T ASSUME that you know which points make opposite sides and you need to find the slope for.

Always sketch a graph!

Determine whether the four

given points are vertices of a

parallelogram.

8. (–1, 1), (–2, –1), (1, –4), (0, –6)

Slope of (–1, 1), (–2, –1)

= =

Slope of (1, –4), (0, –6)

= =

#8 Continued

Slope of (–1, 1), (1, –4)

= =

Slope of (–2, –1), (0, –6)

= =

Yes it is a parallelogram. Both pairs of opposites sides are parallel.

Word Problem9. The trade in value V of a forklift machine after t years of use is V = 16000 – 2000t dollars. Graph this equation with appropriate restrictions on the variables.

Value (y) won’t go below 0, depends on years (x), which also won’t go below 0.

Graph by finding y – intercept & x – intercept.

#9 continued9. V = 16000 – 2000t dollars

y = –2000x + 16000

(0, 16000) & (8, 0) 16000

8timevalu

e

Ticket Out the Door

Determine whether the four given points are vertices of a parallelogram.

(2, 4), (3, 8), (1, –8), (4, 4)

Explain why or why not.

Homework

#302 Pg. 168 #31 – 63 odd