Lesson: 4 – 6 Equations of Lines Applied Geometry Lesson: 4 – 6 Equations of Lines Objective: Learn to write and graph equations of lines.

Linear Equation Any equation whose graph is a straight line. Example y = 2x – 1

y = 2x - 1 m = 2 What is the slope of y = 2x – 1? y – intercept is -1 What other similarities do you notice about the graph and equation? y – intercept is -1

Slope-Intercept Form y = mx + b y = 2x – 1 m is the slope b is the y-intercept y = 2x – 1 m = 2 b = -1

Name the slope and y-intercept of the graph of each equation. b = 5 y = 3 x = -2 m = 0 b = 3 m = undefined b = none

Name the slope and y-intercept of the graph of each equation. 2x – 3y = 18 Has to be in y = mx + b form to name slope and y-intercept. 2x = 3y + 18 m = 2/3 b = -6 2x - 18 = 3y

Name the slope and y-intercept of the graph of each equation. y = -x + 8 y = -1 x + 4y = 24 x = 10 4y = -x + 24 m = -1 b = 8 y = (-1/4)x + 6 m = -1/4 b = 6 m = 0 b = -1 m = undefined b = none

Graph 2x + y = 3 using the slope and y-intercept. Rewrite into slope-intercept form. y = -2x + 3 Step 1: Put a dot on y-intercept. Step 2: Use slope to find another point on the graph. Step 3: Draw line.

Graph –x + 3y = 9 3y = x + 9 y = (1/3)x + 3

Write an equation of the line parallel to y = 2x – 5 that passes through the point (3, 7). Need the slope and y-intercept. m = 2 Fill in slope and ordered pair in y = mx + b, solve for b. y = mx + b Rewrite equation with m & b 7 = 2(3) + b 1 = b y = 2x + 1

y = -3x + 6 m = -3 4 = -3(1) + b 4 = -3 + b y = -3x + 7 7= b Write an equation parallel to the graph of 3x + y = 6 that passes through the point at (1, 4). Need the slope and y-intercept. y = -3x + 6 m = -3 Fill in what you know y = mx + b, solve for b. 4 = -3(1) + b Rewrite equation with m & b 4 = -3 + b y = -3x + 7 7= b

Write an equation perpendicular to the graph of y = (1/4)x + 5 that passes through the point at (-3, 8). Need the slope and y-intercept. m = -4 remember has to be perpendicular. Fill in what you know y = mx + b, solve for b. 8 = -4(-3) + b 8 = 12 + b Rewrite equation with m & b -4 = b y = -4x - 4

Homework Pg. 177 1 – 12 all, 14 – 42 EOE