3.5-3.6 Slopes of Lines and Writing Equations of Lines Slope of non-vertical line

rise y  y m  run x  x 2

1

2

1

• Positive slope • Negative slope

• Zero slope • Undefined slope http://www.analyzemath.com/Slope/S lope.html

Parallel Lines same slope y = 3x + 6 y = 3x - 5

Perpendicular Lines opposite reciprocal slopes

1 y   x2 3

y  3x  6

To write an equation of a line, you need to know two things . . . slope (m) Point (x,y) y = mx + b

Three Types of Problems Write an equation when given: 1) slope m and y-intercept b – Plug-in m and b into y = mx + b

Example: If the slope is -3 and the y-intercept is 5,what is the equation of the line?

Write an equation when given: 2) – –

slope m and a point (x,y) Use point slope formula Plug in the slope and the known point

Example: If the slope is -3 and the line goes through (2,5), what is the equation of the line?

Write an equation when given: 3) two points (x1, y1), (x2, y2) 1.

Use the two points to find the slope

1.

Pick a point and plug it and the slope into point-slope formula

Example: If the line goes through (2,5) and (-2, 2), what is the equation of the line?

1. Find the slope of the line passing through the points A and B

A

B

2. Find the slope of the line passing through the points A and B B A

3. Are Lines 1 and 2 through given points parallel, perpendicular or neither? Justify your answer. Line 1: (-1,-2) (1,2)

Line 2: (-2,0), (0,4)

3. Are Lines 1 and 2 through given points parallel, perpendicular or neither? Justify your answer. Line 1: (0,1) (1,3)

Line 2: (4,-1), (5,2)

4. Are Lines 1 and 2 through given points parallel, perpendicular or neither? Justify your answer. Line 1: (-3,4), (-3, 1) Line 2: (2,1), (5,1)

5. Graph the line parallel to AB that passes through point P. What do they have in common?

B A P

8. Graph the line perpendicular to AB that passes through point P. What can you say about their slopes?

P A

B

11. Write an equation of the line that passes through point P and is perpendicular to the line with the given equation. Justify your answer.

11. Write an equation of the line that passes through point P and is parallel to the line with the given equation. Justify your answer. P (-8, -4), y = 16

12. Write an equation of the line that passes through point P and is parallel to the line with the given equation. Justify your answer. P (0,-1) y = -2x +3

13. Find the value of k based on the description below:

Write an equation for the perpendicular bisector of AB. A(-5,-5) B(3,3) Step 1: Find the midpoint and slope.

Step 2: Write the equation that is perpendicular to AB that passes through the Midpoint.