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Homework LogWed
10/28
Lesson 3 – 1
Learning Objective: To graph linear equations & find slope
Hw: #301 Pg. 168 #1 – 29 odd
10/28/15 Lesson 3 – 1 Linear Equations Day 1
Advanced Math/Trig
Ch 3 TEST onMonday 11/16/15
Ch 3 Quiz onThursday 11/12/15
Learning Objective
To graph linear equations
To find x & y intercepts
To find slope
To find midpoint
Linear Equation: Ax + By = C
Graph by finding: x – intercept y -
intercept(x , 0) (0 , y)let y = 0 let x = 0Solve for x Solve for y
Slope Intercept Form: y = mx + b
Graph y-int (0, b)Use slope (m) to find another point
1. 2x + 3y = 6 Let x=0: 2(0) +3y = 6
3y = 6 y = 2
(0, 2)
Let y=0: 2x +3(0) = 6
2x = 6
x = 3
(3, 0)
X-int
Y-int
Graph intercepts and connect the dots
Graph & Find x & y intercepts
y
x
(0, 2)
(3, 0)
y
x
Graph & Find x & y intercepts
(0, 2)
(2, –3)
y-int
Find x-int: Let y = 0 0 = (2) 0 =( )(2)0 = –5x + 45x = 4x = (, 0)
y = mx + b
b = 2 (0, 2)
𝑚=−52
or 2.
3. Graph 3y = – 6x
x & y intercept both at (0, 0)
Get into y = mx + b
3y = – 6x
y = – 2x
m = y – int (0, 0)
Graph & Find x & y intercepts
y
x
Two Special Cases
x = -3 (no y)
y = 2 (no x)I only see an
“x” It
goes thru
x-axis
I only see a “y”
It goes thru y-
axis
y
x
Vertical line thru (-3, 0)
Undefined Slope
Horizontal line thru
(0, 2)Zero Slope
ZeroUndefined
4. Graph 3x = 12It ONLY has x, so
solve for x.
3x = 12x = 4
x ALWAYS equals 4
Graphing vertical lines
5. Graph a line with slope of 0 and goes through (-3, 4)
Slope = 0
Horizontal Line
at y = 4
Slope Formula
Given 2 points: (x1, y1) and (x2, y2)
The slope of the line through the points is
𝑆𝑙𝑜𝑝𝑒=𝑚= 𝑟𝑖𝑠𝑒𝑟𝑢𝑛
=𝑦2− 𝑦1
𝑥2− 𝑥1
6. Find slope (3, -5) (7, -2)
(x1, y1) (x2, y2)
Find Slope
Special Cases = 0
= undefined
way!
7. (3, 1) & (– 4, 1)
horizontal line!
At y = 1
Find Slope
8. (7, 3) & (7, 1)
vertical line!
at x = 7
Find Slope
CANNOT DIVIDE BY ZERO!!
Midpoint Formula
1 1 2 2
1 2 1 2
Given ( , ) , ( , )
Find the midpoint
,2 2
x y x y
x x y y
Find Midpoint9. (4, 0) & (– 10, 3)
(x1, y1) (x2, y2)
Midpoint =
=
=
Find Midpoint10. (a, b) & (– a, b)
(x1, y1) (x2, y2)
Midpoint =
=
=
=
Find Midpoint11. (, 0) & (, 0)
(x1, y1) (x2, y2)
Midpoint =
=
=
=
=
=
=
=
Ticket Out the Door
None today!
Homework
#301 Pg. 168 #1 – 29 odd