Intensive Math-Algebra I Mini Lesson MA.912.A.3.10
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1 Intensive Math-Algebra I Mini Lesson M Summer 2013 Writing Equations of Perpendicular Lines Student Packet Day 10
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3 Name: Date: Benchmark M Write an equation of a line given any of the following information: two points on the line, its slope and one point on the line, or its graph. Also, find an equation of a new line parallel to a given line, or perpendicular to a given line, through a given point on the new line. Also assesses M Rewrite equations of a line into slope-intercept form and standard form. Also assesses M Graph a linear equation or inequality in two variables with and without graphing technology. Write an equation or inequality represented by a given graph. Also assesses M912.G.1.4 Use coordinate geometry to find slopes, parallel lines, perpendicular lines, and equations of lines. This benchmark will be assessed using MC and FR items. Students will: Write equations, including lines parallel or perpendicular to a given line. Rewrite equations of lines from standard form to slope-intercept form, and vice versa. Identify a linear inequality in slope-intercept form, given a graph. Content Limits Information given to determine equations of lines may include two points, the slope and a point, a graph, or an equation in a different form. Items may include lines that have zero slope or undefined slope. Given coordinates will be limited to rational numbers. Lesson M Textbook: Prentice Hall Algebra 1 I can Write an equation of a line given 2 points, the slope and a point, or a graph. Determine the slope of a line perpendicular to a given line. Determine the equation of a line perpendicular to a given line. Vocabulary Perpendicular Slope Intercepts Standard Form Slope-Intercept Form Point-Slope Form Coordinate Essential Understanding Perpendicular lines intersect at 90-degree angles. The slopes of perpendicular lines are negative reciprocals.
4 Example # 1: Textbook page 328 Guided Practice: Textbook page 331: Example # 2: Textbook page 329 Guided Practice: Textbook page 331: 13-18, and 27 Small Group Practice: Focus MA912A310 Mini-Assessment MA912A310 (Perpendicular Lines) Score: Home Learning: HL MA912A310 (Perpendicular Lines)
5 Focus Practice M (Perpendicular Lines) 1. The line shown in the graph below can be represented by the equation. Write the equation for a line that is perpendicular to this line, passing through the point? 2. Line passes through the points (2, 7) and (6, 1). Line t passes through the point (5, 2) and is perpendicular to line. Write the equation for line t 3. The line shown in the graph below can be represented by the equation. Write the equation for a line that is perpendicular to the one in the graph and passes through the point? 4. Line passes through the points (1, 4) and (4, 9). Line m passes through the point (3, 2) and is parallel to line. What is the equation for line m?
6 5. A right triangle has two sides that are perpendicular to each other. Triangle PQR has vertices P Q ), and R 0. Determine whether PQR is a right triangle. 6. In a rectangle, opposite sides are parallel and adjacent sides are perpendicular. Figure ABCD has vertices A B C 0 and D 5. Show that ABCD is a rectangle.
7 Home Learning M : Writing Equations of Perpendicular Lines 1. Determine the equation of a line that is perpendicular to the line and that passes through the point (10, 0). y = y = y = y = 2. Determine the equation of a line that is perpendicular to the line y = and that passes through the point 3. Which equation describes a line that passes through and is perpendicular to the line described by? 4. Which equation describes a line perpendicular to?
8 5. Given, determine which two points are on a line perpendicular to. 6. The graph of line is shown below. Which of the following is an equation for a line that is perpendicular to line in the graph? 7. A line has a slope of and a y-intercept of 6. Which of the following is an equation of the line?
9 8. Which equation describes a line that passes through (6,-8) and is perpendicular to the line described by 4?
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