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

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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 y = mx + b m – slope b – y-intercept Point-Slope Form y – y 1 = m(x – x 1 ) m – slope (x 1, y 1 )

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

y = ½ x + 8 Graphing Graph (0, 8) Up 1 over 2 Write an equation in slope-intercept form of the line with slope ½ and y- intercept of 8. Then graph the line. 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 1: Find the slope m = 2 Use slope-intercept form Pick one of the points 3 = 2(0) + b b = 3 y = 2x + 3 Method 2: Find the slope m = 2 Use point-slope form Pick one of the points y – 3 = 2(x – 0) Solve for y to put in slope-intercept form. y – 3 = 2(x – 0) y – 3 = 2x y = 2x + 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 slope- intercept form. Find the slope m = 0 (horizontal line) 6 = 0(-2) + b 6 = b y = 0x + 6 y = 6 Make sure you simplify. Do not leave 0x 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 The line goes through the axis of the variable given. A horizontal line at 6 through the y-axis.

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

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

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

Homework Pg – 12 all, 14 – 40 E