Homework Log Wed 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 Quiz on Thursday 11/12/15 Ch 3 TEST on Monday 11/16/15

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 = 0 Solve for x Solve for y Slope Intercept Form: y = mx + b Graph y-int (0, b) Use slope (m) to find another point 𝑚= 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛

Graph & Find x & y intercepts Let x=0: 2(0) +3y = 6 3y = 6 y = 2 (0, 2) y x Y-int (0, 2) Let y=0: 2x +3(0) = 6 2x = 6 x = 3 (3, 0) (3, 0) X-int Graph intercepts and connect the dots

Graph & Find x & y intercepts b = 2  (0, 2)  y-int 𝑚=− 5 2 y = mx + b 𝑢𝑝 𝑙𝑒𝑓𝑡 or 𝑑𝑜𝑤𝑛 𝑟𝑖𝑔ℎ𝑡 y x Find x-int: Let y = 0 0 = − 5 2 𝑥+2 (2) 0 =( − 5 2 𝑥+2 )(2) 0 = –5x + 4 5x = 4 x = 4 5 ( 4 5 , 0) (0, 2) (2, –3)

Graph & Find x & y intercepts 3. Graph 3y = – 6x x & y intercept both at (0, 0) Get into y = mx + b 3y = – 6x y = – 2x m = − 2 1 𝑢𝑝 𝑙𝑒𝑓𝑡 y – int (0, 0)

Two Special Cases x = -3 (no y) y = 2 (no x) Undefined Zero I only see an “x” It goes thru x-axis x = -3 (no y) I only see a “y” It goes thru y-axis y = 2 (no x) y x y x Undefined Zero Vertical line thru (-3, 0) Undefined Slope Horizontal line thru (0, 2) Zero Slope

Graphing vertical lines 4. Graph 3x = 12 It ONLY has x, so solve for x. 3x = 12 x = 4 x ALWAYS equals 4

5. Graph a line with slope of 0 and goes through (-3, 4) Slope = 0 Horizontal Line at y = 4

Slope Formula 𝑆𝑙𝑜𝑝𝑒=𝑚= 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛 = 𝑦 2 − 𝑦 1 𝑥 2 − 𝑥 1 Given 2 points: (x1, y1) and (x2, y2) The slope of the line through the points is 𝑆𝑙𝑜𝑝𝑒=𝑚= 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛 = 𝑦 2 − 𝑦 1 𝑥 2 − 𝑥 1

Find Slope 6. Find slope (3, -5) (7, -2) (x1, y1) (x2, y2) 𝑚= 𝑦 2 − 𝑦 1 𝑥 2 − 𝑥 1 = −2−(−5) 7−3 = −2+5 4 = 3 4

Special Cases m= 0 # = 0 m= # 0 = undefined 0 𝐾 𝑁 0 way!

Find Slope 𝑚= 𝒚 𝟐 − 𝒚 𝟏 𝒙 𝟐 − 𝒙 𝟏 7. (3, 1) & (– 4, 1) 𝑚= 𝒚 𝟐 − 𝒚 𝟏 𝒙 𝟐 − 𝒙 𝟏 = 𝟏−𝟏 −𝟒−𝟑 = 𝟎 −𝟕 =𝟎 horizontal line! At y = 1

Find Slope 𝑚= 𝒚 𝟐 − 𝒚 𝟏 𝒙 𝟐 − 𝒙 𝟏 8. (7, 3) & (7, 1) 𝑚= 𝒚 𝟐 − 𝒚 𝟏 𝒙 𝟐 − 𝒙 𝟏 = 𝟏−𝟑 𝟕−𝟕 = −𝟐 𝟎 =𝒖𝒏𝒅𝒆𝒇𝒊𝒏𝒆𝒅 vertical line! at x = 7 CANNOT DIVIDE BY ZERO!!

Midpoint Formula

Find Midpoint 9. (4, 0) & (– 10, 3) (x1, y1) (x2, y2) = 4+(−10) 2 , 0+3 2 = −3, 3 2

Find Midpoint 10. (a, b) & (– a, b) (x1, y1) (x2, y2) = 𝑎+(−𝑎) 2 , 𝑏+𝑏 2 = 0 2 , 2𝑏 2 = 0, 𝑏

Find Midpoint 10𝜋 4 2 = 10𝜋 4 ÷2 = 10𝜋 4 ∙ 1 2 = 10𝜋 8 = 5𝜋 4 11. ( 𝜋 4 , 0) & ( 9𝜋 4 , 0) (x1, y1) (x2, y2) Midpoint = 𝑥 1 + 𝑥 2 2 , 𝑦 1 + 𝑦 2 2 = 𝜋 4 + 9𝜋 4 2 , 0+0 2 = 10𝜋 4 2 , 0 2 = 5𝜋 4 ,0 10𝜋 4 2 = 10𝜋 4 ÷2 = 10𝜋 4 ∙ 1 2 = 10𝜋 8 = 5𝜋 4

Ticket Out the Door None today!

Homework #301 Pg. 168 #1 – 29 odd