Rectangular Cooordinate System

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1 Chapter 3 Analytical Algebra 2 1 Rectangular Coordinate system Rectangular Cooordinate System Axes Ordered pairs x-coordinate y-coordiante Graph an ordered pair Origin Quadrants. Page 138 3, 4, 5, 6 Find the distabnce between the points: (2, 4) and (-5, 4) Distance and Midpoint (2, -1) and (2, 3)

2 Chapter 3 Analytical Algebra 2 2 (3, 4) and (0, 0) (2, 1) and (-1, 5) The Distance Formula Line Line segment Length of a line segment Midpoint Find the midpoint of the line segment whose indpoints are (2, 4) and (5, 4)

3 Chapter 3 Analytical Algebra 2 3 Find the midpoint of the line segment with endpoints ( -5, 4) and ( -3, 2) The Midpoint Formula Find the midpoint of the line with endpoints (-3, -5) and (-2, 3) Page , 27, 30 Solve y + 1 = 2x Graphs of Linear Equations How many solutions? What do they look like? How can we represent them?

4 Chapter 3 Analytical Algebra 2 4 Graph the equation y = -3x + 2 NOTE: When we graph an equation we are Why is y = -3x + 2 called a linear equation? Graph 4x y = 4 Graph 6 + 2y = -2 Page 174 5, 6, 8, 15, 16, 17

5 Chapter 3 Analytical Algebra 2 5 Graph the equation y = 4 Graph the equation x = -2 Page Intercepts x-intercept (, ) y-intercept (, ) Find the x and y intercepts, if they exist, for: y = 2x + 1 To find intercepts: x-intercept yintercept

6 Chapter 3 Analytical Algebra 2 6 Find, if they exist, the x-intercept and y-intercept for 3x + 4y = -12. Page , 30, 33, 36 Slope Slope of a line Slope Formula Remember our fraction rules. Find the slope of line which passese through the points: (2, 4) and (4, 5) (-1, 2) and (3, -4)

7 Chapter 3 Analytical Algebra 2 7 Find the slope of the line which passes through thepoints: (3, 2) and (-4, 2) (2, 3) and (2, -4) Every horizontal line has: An equation of: A slope of. Every vertical line: An equation of: slope. A line which slants downward has slope. A line which slants upwards has slope. Page 186 3, 5, 7, 11, 15 Draw the graph of the line which passes through the point (-4, 2) and which has a slope of 3.

8 Chapter 3 Analytical Algebra Note : 3 = = ---- = 4 Draw the graph of the line which passes through: the point (0, 4) and which has a slope of 2/3. the point (-3,0) and which has a slope of -3/4. Graph the equation y = 5/3x 4 We can graph by finding three / solutions. Or We can graph by recognizing that... Graph the equation x + 2y = 4 Graph the equation 3 y x 4 2 Page , 33, 37, 38, 42, 44

9 Chapter 3 Analytical Algebra 2 9 More with Slopes Horizonatl lines have slope. Vertical lines have slope Upward slanting lines have slopes. Downward slating lines have slopes. Steep lines have slopes, greater than ( in absolute value ) Slow rising lines have slopes, less than ( in absolute value ) Sketch a line with the given slopes: 3 ½ /5 1-7/2 9/4 A positive slopes means that as x increases, y, or as x decresases, y A negative slope means that as x increase, y, or as x decreases, y. Solve for x: 4 x x 1 3 5

10 Chapter 3 Analytical Algebra 2 10 A line with a slope of 2/5 passes through the points (4, 3) and (-1, y). Find y. A line with slope -3, passes though the points (x, 3) and (0, 6). Find x. a line passes through the points ( -4, 7), (4, 1) and ( x, 4). Find x. Page

11 Chapter 3 Analytical Algebra 2 11 Writing Equations of Lines y = 2x + 3 2x 3y = 9 x = 4y 7 2x 3 + 3y = 4x 7y + 10 y 3 = 2(x + 4) x 2 y = 9 There are a few different forms of a line that we can use, we will focus on tow of them. Slope-intercpt form Point-slope form Standard form Write an equation of the line: Passing through the point (0, 3) with a slope of 4. Passing through the point (2, 0) with a slope of -2/3

12 Chapter 3 Analytical Algebra 2 12 Passing through the point (-2, 4) with m = -4 Passing through the points (0, 4) and (3, 5). Passing through the points (-1, 1) and (4, 4) Page 194 3, 5, 7, 11, 17, 29, 37, 38 Graph the line y = 4 Wirte the equation of the line which passes through the point (2, 4) and has slope = 0.

13 Chapter 3 Analytical Algebra 2 13 Write the equation of the line which passes through the point (-2, 4) and has no slope. Write the equation of the line which passes through the points (-2, 3) and (4, 3). Write the equation of the line which passes through the points (-2, 3) and (-2, 3). All horizontal lines, lines with a slope of, have equations: All vertical lines, lines with slope, have equations : Page , 21, 25, 43, 47, 49

14 Chapter 3 Analytical Algebra 2 14 Parallel and Perpendicular Lines In geometry: Parallel lines Perpendicular lines In algebra: Parallel lines Perpenduclar lines Are the lines, one passing though the points (-2, 1) and (-5, -1) and the other passing through the points (1, 0) and (4, 2), parallel, perpendicular, neither or both?

15 Chapter 3 Analytical Algebra 2 15 Are the graphs of the lines, y= 3/2x 5 and 2x + 3y = 6, parallel, perpendicular or netiher? Write an equation of a line perpendicular to the line y = 4x + 5, which passes through (0, 2). Write a n equation of the line which passes through the point (2, 3) and which is parallel to the line y = 1/2x 4. Write the equation of the line which passes through the point (3, -4) and which is perpendicular to the line 2x y = -3.

16 Chapter 3 Analytical Algebra 2 16 What slope does a line have, which is perpendicular to a line with slope of 0 have? Write the equation of the line which is parallel to the line x = 5 and which passes thorugh the point (3, 1). Write the equation of the line which is perpendicular, to the line x = 5 and which passes through the point (5, 2). Page 203 3, 5, 11, 13, 19, 21, 23, 27, 29

17 Chapter 3 Analytical Algebra 2 17 How many solutions does y + 4 = 3 have? How many solutions does y = x 1 have? How many solutions does y > x 1 have? The graph of the solutions to y = x 1 creates a. The graph of the solutions to y > x 1 creates a. Graph y > x 1 Graph x 2y 4

18 Chapter 3 Analytical Algebra 2 18 Graph y < -x + 2 Graph x > -1 Graph y 3 Page , 13, 14, 19, 20

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