Graphing Lines Dr. Carol A. Marinas

Graphing Lines Plotting Points on a Coordinate System Graphing a line using points Graphing a line using intercepts Finding the slope Graphing a line using slope and a point Graphing a line using slope and y-intercept Horizontal & Vertical Lines Parallel & Perpendicular Lines Equations of a Line

Plotting points on a coordinate system (x, y) x moves left or right & y moves up or down (1, 1) is right 1 and up 1 (-2, -1) is 2 to the left and 1 down

Graphing a line using points Make a table finding at least 3 points Example: 2x + y = 4 x y 1 2 -1 6 3 -2

Graphing a line using intercepts Make a table Example: 2x + y = 4 X-intercept put 0 in for y and solve for x. 2x + 0 = 4 x = 2 (2, 0) is x-intercept y-intercept put 0 in for x and solve for y. 2(0) + y = 4 y = 4 (0, 4) is y-intercept x y 4 2

Finding the slope given 2 points m = Find the slope of the line connecting (-2,1) and (6, -3) m = -3 - 1 = -1 6 - (-2) 2

Graphing Using the Slope and a Point Graph the point Do the slope from that point (up/down for numerator and left/right for denominator) Follow same pattern for more points Draw the line Example: Point (1, -2) & m= 1/3

Graphing line using the slope and y-intercept Graph y-intercept Do slope (up/down, left/right) Draw line Example: y-intercept (0, 2) m = 3/2

Horizontal & Vertical Lines y = c where c is a constant Horizontal line y-intercept (0, c) Slope is 0 x= c where c is a constant Vertical line x-intercept is (c, 0) Slope is undefined or NO slope

Parallel & Perpendicular Lines Parallel lines have the same slope Example: y = 2x + 1 y = 2x -4 Both have a slope of 2, therefore the lines are parallel Perpendicular lines have slopes whose product is -1. Example: y = 3x + 2 y = -1/3 x - 4 First has slope of 3 and second has a slope of -1/3. 3 * -1/3 = -1

Equations of a Line Ax + By + C = 0 (General Form - no fractions for A, B, or C) y = mx + b (Slope - intercept form) m is the slope and (0, b) is the y-intercept y - y1 = m (x - x1) (Point - slope form) (x1, y1) is a point and m is the slope

Questions about Lines Find the equation of a line in GENERAL FORM through (-2, 2) and (1, 3) Find the equation of a line in Slope-intercept form through (6, -2) and parallel to 3x - 2y =4 Find the equation of the line with a slope of 0 and a y-intercept of (0, -3) Find the equation of a line in Slope-intercept form and through (4, 3) & perpendicular to 2x = 4y + 6

Answers to Lines Slope = 3 - 2 = 1 Find the equation of a line in GENERAL FORM through (-2, 2) and (1, 3) Slope = 3 - 2 = 1 1- (-2) 3 Using Point-slope equation: y - 2 = 1/3 (x - -2) y - 2 = 1/3 x + 2/3 3y - 6 = x + 2 -x + 3y -8 = 0 OR x - 3y + 8 = 0

Answers to Lines Find the equation of a line in Slope-intercept form through (6, -2) and parallel to 3x - 2y = 4 Find the slope of 3x - 2y = 4 by solving for y. -2y = -3x + 4 y = 3/2 x - 2 m = 3/2 (Parallel lines have the same slope) Using Point-slope equation: y - (- 2) = 3/2 (x - 6) y + 2 = 3/2 x - 9 y = 3/2 x - 11

Answers to Lines Find the equation of the line with a slope of 0 and a y-intercept of (0, -3) Find the equation of a line in Slope-intercept form and through (4, 3) & perpendicular to 2x = 4y + 6 Slope of 0 means this is a horizontal line in the form y = c. So y = -3 Find slope of 2x = 4y + 6 by solving for y. y = 1/2 x - 3/2 Slope of perpendicular line is -2. (Because 1/2 * -2 = -1) y - 3 = -2 (x - 4) y = -2x + 11

Hope you enjoyed Lines !