Presentation on theme: "4.3 Writing equations of parallel and perpendicular lines"— Presentation transcript: 1 4.3 Writing equations of parallel and perpendicular lines 2 Core Concept Parallel lines lie in the same plane and never intersect. 3 Example 1 –
identifying parallel lines
4 Example 2 – Writing an Equation of a parallel line
5 You Try! 1. Line a passes through (-5, 3) and (-6, -1). Line b passes through (3, -2) and
(2, -7). Are the lines parallel? Explain. 2. Write an equation of the line that passes through (-4, 2) and is parallel to the line y = ¼ x +1 . No, they do not have the same slope. 2 = ¼ (-4) + b 2 = -1 + b 3 = b y = ¼ x + 3
6 Example 3 – identifying parallel and perpendicular lines 7 Example 4 – Writing an Equation of a perpendicular line 8 You Try! 3. Determine which of the lines, if any, are parallel, or perpendicular. Line a: 2x + 6y =
-3 Line b: y = 3x – 8 Line c: -6y + 18x = 9 4. Write an equation of the line that passes through (-3, 5) and is perpendicular to the line y = -3x -1, Lines b and c are parallel. Line a is perpendicular to lines b and c. y = 1/3 x + 6 9 Example 5 – Writing an equation of a perpendicular line
10 Understand the Problem – You are asked to write an equation
that represents the shortest path from the helicopter to the shoreline. (perpendicular distance) Make a plan – to write an equation for a perpendicular line you must: find the slope of the shoreline, find the opposite reciprocal slope. Then use point-slope form with the coordinate (14,4) to write the equation.
11 Complete the plan – The slope of the shoreline passes through the points (1, 3) and (4, 1) so, the slope is: 𝑚= 1−3 4−1
= −2 3 The opposite reciprocal slope is 12 Use the slope m = 3 2 and (14, 4) with the point-slope form. 13 You try! 5. In Example 5, a boat is traveling
parallel to the shoreline and passes through (9, 3). Write an equation that represents the path of the boat. boat (9,3) 𝑦= −2 3 𝑥+9 |