Lesson 4 ­ REVISED Review of Equations of Lines complete.notebook March 06, 2020 March 6, 2020 Review of Equations of Lines WARM UP: a) Find the midpoint of: (8 , ­2) and (­5 , 7) b) A(­2,­6) is the endpoint and B(0 , 3) is the midpoint on line AC. Find the endpoint C. Review: Slope of a Line Calculate the slope of the line joining points (­6, 4) and (2, ­8). Using the graph.... m = rise run Using the ordered pairs.... m = y2 ­ y1 x2 ­ x1 1 Lesson 4 ­ REVISED Review of Equations of Lines complete.notebook March 06, 2020 Review: Equations of Lines There are two main forms of the equation of a line. 1) slope and y­intercept form: y = mx + b 2) standard form: Ax + By + C = 0 • all terms are on one side of the equation • the coefficient of x must be positive • NO fractions . Finding the Equation of a Line To write the equationof a line, we need to know... * * 2 Lesson 4 ­ REVISED Review of Equations of Lines complete.notebook March 06, 2020 The Various Scenarios... 1) THE SLOPE AND Y­INTERCEPT ARE KNOWN. To determine the equation of the line, substitute directly into y = mx + b. eg. a) The slope is ­4 and the y­intercept is 9. b) The slope is ½ and the y­intercept is ­7. 2) THE SLOPE AND A POINT ON THE LINE ARE KNOWN. • Find the y­intercept by substituting the point and slope into y = mx + b and solve for b. • Once both the slope and y­intercept are known, substitute directly into y = mx + b. eg. a) The slope is 3 and point (­1, 4) is on the line. b) The slope is ­¾ and point (2, ­7) is on the line. 3 Lesson 4 ­ REVISED Review of Equations of Lines complete.notebook March 06, 2020 3) TWO POINTS ON THE LINE ARE KNOWN. • Find the slope using, m = • Find the y­intercept by substituting the slope and one point into y = mx + b and solve for b. • Once both the slope and y­intercept are known, substitute directly into y = mx + b. eg. a) The line passes through (­6, ­2) and (4, 3). b) The line passes through (7, ­10) and (3, 8). Review: Horizonatal and Vertical Lines Horizontal Lines • written in the form y = # • slope is equal to ZERO Determine the equation of a horizontal line through the point (2, ­7). Vertical Lines • written in the form x = # • slope is UNDEFINED Determine the equation of a vertical line through the point (2, ­7). 4 Lesson 4 ­ REVISED Review of Equations of Lines complete.notebook March 06, 2020 Review: Parallel and Perpendicular Lines Parallel lines have the same slope. Perpendicular lines have slopes that are negative reciprocals. eg. eg. 1. Determine the equation of a line that is parallel to 3x ­ 5y = 10 and passes through the point (4, ­5). 2. Determine the equation of the line that is perpendicular to x ­ 3y ­ 1 = 0 and passes through the point (­3, 1). 5 Lesson 4 ­ REVISED Review of Equations of Lines complete.notebook March 06, 2020 Review: • Handout…Finding the Equation of a Line Equations of Lines **Quiz ... Monday** ­ length of line ­ equation of circle ­ midpoint of a line 6