Graphing Linear Equations 4.2 Objective 1 – Graph a linear equation using a table or a list of values Objective 2 – Graph horizontal or vertical lines

Graphing a Linear Equation a linear equation is a straight line.

y x Use the graph to decide whether the point lies on the graph of x + 3y = 6 a)(1, 2) b)(-3, 3) c)(0, 2) EXAMPLE 1 Verifying Solutions of an Equation a) x + 3y = (2) = 6 7 = 6 b) x + 3y = (3) = 6 6 = 6 c) x + 3y = (2) = 6 6 = 6 ? ? ? / no yes

EXAMPLE 2 Graphing an Equation y + 2 = 3x y = 3x – Choose x Substitute to find y y = 3x - 2 (-2, -8) (-1, -5) (0, -2) (1, 1) (2, 4) y = 3(-2) – 2 = -8 y = 3(-1) – 2 = -5 y = 3(0) – 2 = -2 y = 3(1) – 2 = 1 y = 3(2) – 2 = 4 solve for y (x, y)

EXAMPLE 3 Graphing a Linear Equation y – 1 = 2x y = 2x Choose x Substitute to find y y = 2x + 1 (-2, -3) (-1, -1) (0, 1) (1, 3) (2, 5) y = 2(-2) + 1 = -3 y = 2(-1) + 1 = -1 y = 2(0) + 1 = 1 y = 2(1) + 1 = 3 y = 2(2) + 1 = 5 (x,y)

Horizontal and Vertical lines y x y x y = b x = a In the coordinate plane, the graph of y = b Is a horizontal line In the coordinate plane, the graph of x = a Is a vertical line

EXAMPLE 5 Graphing y = b y x Graph y = 2 xy y = 2

EXAMPLE 6 Graphing x = a y x Graph x = -3 xy x = -3