Geometry Lesson 3 4 Equations of Lines Objective

Geometry Lesson 3 – 4 Equations of Lines Objective: Write an equation of a line given information about the graph. Solve problems by writing equations.

Equation Forms Slope-Intercept Form ly = mx + b l m – slope l b – y-intercept Point-Slope Form ly – y 1 = m(x – x 1) l m – slope l (x 1, y 1)

Write an equation in slopeintercept form of the line with slope 3 and y-intercept of – 2. Then graph the line. y = mx + b y = 3 x – 2 Graphing: l Put a dot on the y-intercept l l (0, 3) Use slope (rise/run) to find more points. l Up 3 over 1

Write an equation in slope-intercept form of the line with slope ½ and yintercept of 8. Then graph the line. y=½x+8 Graphing l Graph (0, 8) l Up 1 over 2 Don’t have to go by 2’s

Write an equation in point-slope form of the line with slope – 3/4 that contains (-2, 5). Then graph. y – y 1 = m(x – x 1) (x – (-2)) Graphing: plot point, then use slope

Write an equation in point-slope of the line with slope of 4 that contains (-3, -6). Then graph. y + 6 = 4(x + 3)

Write an equation of the line through each points in slope-intercept form (0, 3) and (-2, -1) Method 2: Find the slope Method 1: Find the slope l l m=2 Use slope-intercept form l l l Pick one of the points 3 = 2(0) + b b=3 y = 2 x + 3 m=2 Use point-slope form l l Pick one of the points y – 3 = 2(x – 0) Solve for y to put in slope-intercept form. l l y – 3 = 2(x – 0) y – 3 = 2 x y = 2 x + 3 You may use either method

Write an equation of the line through each points in slope-intercept form (-2, 4) & (8, 10)

Write an equation of the line through (-2, 6) & (5, 6) in slopeintercept form. Find the slope l m = 0 (horizontal line) 6 = 0(-2) + b 6=b y = 0 x + 6 y=6 Make sure you simplify. Do not leave 0 x or 0

Horizontal & Vertical Lines When an equation only has 1 variable it is either a horizontal or vertical line The equation tells you how to graph. y=6 l The line goes through the axis of the variable given. l A horizontal line at 6 through the y-axis. l

Tell whether the following is a horizontal or vertical line. y = 3 horizontal x = 6 vertical x = -1 vertical 5=y horizontal -9 = x vertical x=0 Vertical (y-axis) y=0 Horizontal X-axis

Write an equation in slope-intercept form for a line perpendicular to the line y = -3 x + 2 through (4, 0). Step 1: Identify slope for new equation l m = 1/3 (because of perpendicular) Write new equation with new slope and point. l

Write an equation is slopeintercept form for a line parallel to y = (-3/4)x + 3 containing (-3, 6) Step 1: Identify slope for new equation l (-3/4) same slope since parallel Write new equation with new slope and point.

Homework Pg. 200 1 – 12 all, 14 – 40 E