3.1 Graphing in 2-D Coordinates (Day 1) Today’s Date: 10/30/17 Ch 3 TEST on Wed 11/15

Linear Equation: Ax + By = C To Graph: Find the x- and y-intercepts (x , 0) (0 , y) let y = 0 let x = 0 Solve for x Solve for y

Slope Intercept Form: y = mx + b To Graph: Graph y-int (0, b) Use slope (m) to find another point

Ex 1) Graph 2x + 3y = 6 & Find x- and y-int 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) Y-int X-int Graph intercepts and connect the dots

Graph (0, 2) and (3, 0) and connect dots y x (0, 2) (3, 0)

Ex 2) Graph & find x- and y-int y = mx + b Ex 2) Graph & find x- and y-int  y-int Find x-int: Let y = 0 y x (0, 2) (2, –3)

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

Slope Formula Given 2 points: (x1, y1) and (x2, y2) The slope of the line through the points is

Ex 3) Find the slope of the line through (- 3, - 4) and (7, - 2) x1 y1 x2 y2

Special Cases

Midpoint Formula

Ex 4) Find the midpoint of (4, 0) and (- 10, 3) x1 y1 x2 y2

Homework #301 Pg. 168 1 – 29 odd

3.1 (Day 2) Graphing in 2-D Coordinates Today’s Date: 10/31/17

Given Ax + By = C, find slope Ex 1) Find the slope of 4x – 2y = 20 A = 4 B = –2

OR Rewrite in Slope-Intercept Form y = mx + b and find slope (m) 4x – 2y = 20 –2y = –4x + 20 y = 2x – 10 m = 2

Set each coordinate part = to each other Ex 2) Midpoint = (–2, 7) & One Endpoint = (3, –5). Find other endpoint. (x1 , y1) Find (x2 , y2) Set each coordinate part = to each other

And solve for x and y: Other endpoint: (–7, 19)

Ex 3) Suppose the 3 points lie on a straight line. Find missing coord. (1, –1), (–2, 8), (x, –7) Find slope, use (1, -1) & (-2, 8): Use slope & these 2 points (-2, 8) & (x, -7):

Make a table and plug values into y and solve for x Ex 4) Sketch the graph of Plug in -2, -1, 0, 1, 2 into y Make a table and plug values into y and solve for x y x x │y│ – 1 y 1 –1 │–2│–1 │–1│ – 1 │0│ – 1 │1│ –1 │2│ – 1 –2 –1 1 2

Plug values into y & solve for x Ex 5) Sketch graph of Plug in -2, -1, 0, 1, 2 into y Plug values into y & solve for x y x x y2 + 1 y 5 2 1 (–2)2 + 1 (–1)2 + 1 (0)2 + 1 (1)2 + 1 (2)2 + 1 –2 –1 1 2

HINT for Homework: Parallelogram (HW #51 & 53) To determine vertices of Parallelogram: Draw Sketch Opp. Sides are parallel → same slope (m)

Homework #302 Pg. 168 31 - 63 odd