1. Graphing Lines
Dr. Carol A. Marinas

2. 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

3. 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

4. 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

5. Graphing a line using intercepts
Make a table
Example: x + 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

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

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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

13. Answers to Lines Slope = 3 - 2 = 1
Find the equation of a line in GENERAL FORM through (-2, 2) and (1, 3)
Slope = = 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

14. Answers to Lines
Find the equation of a line in Slope-intercept form through (6, -2) and parallel to x - 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

15. 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

16. Hope you enjoyed Lines !