3.1 Graphing in 2-D Coordinates

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