graphing lines dr. carol a. marinas. graphing lines plotting points on a coordinate system graphing...
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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 = 4x 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 = 4x = 2(2, 0) is x-intercept
y-intercept put 0 in for x and solve for y.
2(0) + y = 4y = 4(0, 4) is y-intercept
x y
0 4
2 0
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
12
12
xx
yy
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 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 + 2/33y - 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 !