Class Notes and Work
Directions: Using the following formula, find the slope
for each of the following pairs of coordinates.
y1
– y2
x1 – x2
1. (3,5), (4,7) 2. (2,1), (1,3)
3. (6,7), (7,6) 4. (0,0), (-3, -9)
5. (4, 1), (4, 10) 6. (-5, -9), (7,-9)
7. (4, 2), (2, 1) 8. (10,3), (4,9)
9. (0,2), (2,10) 10. (-2,-5), (-3,1)
Now, use the following formula, y - y1 = m(x - x1), to find the equation, y = mx + b, for each of the pairs.
Example:
(3,4), (2,7) Label your pairs with x,y and determine which one is larger with a “check” mark to determine if it is a positive or negative slope. 3 is bigger than 2 and 7 is bigger than 4, There will be a “check” mark in each of the pair. Therefore, this is a negative slope. Then label each pair with “1” or “2.”
y1
– y2 =
7 - 4 = 3 = -3 = m
x1 – x2 2 -
3 -1
y - y1 = m(x - x1) = y – 7 = -3(x – 2) Don’t forget to distribute the -3.
y – 7 = -3x +6 Add 7 to both sides.
y = -3x + 13
Parallel and Perpendicular Lines
Example: y = 2x – 5
Parallel lines will have the same slope = 2. Just change the y-intercept.
Therefore, a line parallel to y = 2x -5 can be y = 2x + 6, y = 2x + 7, y = 2x - 7.
Perpendicular lines will have slopes that are negative reciprocals of each other ---- -1/2
A line that is perpendicular to y = 2x – 5 can be y = -1/2x -7. Again, change the y-intercept and this time the slope also get changed.
