Warm-up Warm-up Warm-up Warm-up

1. Write the equation of a line given m = 1/4 1. Write the equation of a line given m = 1/4 and thru the point (12,-6).and thru the point (12,-6).

2. Write the equation of a line thru these two 2. Write the equation of a line thru these two points. A(6,15) and B(-12, 12) .points. A(6,15) and B(-12, 12) .

3.3. Write the equation of a line that is parallel to Write the equation of a line that is parallel to

y = 2x – 3 thru this point. A(-2,7).y = 2x – 3 thru this point. A(-2,7).

HW: WS 7.1B

Answers: 1. y = 1/4x -92. y = 1/6 x + 143. y = 2x + 11

Lesson 7.1B Writing equations for lines that are perpendicular to a given line.

Perpendicular Slopes are opposite reciprocals.

• Original

1/8

-3

• Opposite reciprocal

-8

1/3

2

3 3

2

More Examples:

Find the slope of the given line and then find the slope of any lines perpendicular to that line.

m = 7

m = 3/2

m = -1

11. 5

7

22. 6

3

3. 5

y x

y x

y x

Parallel, Perpendicular, Coinciding, or intersecting but not

perpendicular?4) Y = 2x + 2 5) Y = 3x -6

Y = 2x - 2 Y = -6 + 3x

6) 7)

y = 5x - 8 y = 3x + 7

m = 2, m = 2 parallel m = 3/1, m= 3/1 coinciding

m = -1/5, m = 5/1 perpendicular

m = 2/3, m= 3/1 intersecting

12

5y x 2

73

y x

Example 1: Write the equation of the line that is perpendicular to

y = 2x – 3 and goes through (6, -4)Original m = 2, opposite

reciprocal m = -1/2• -4 = -1/2(6) + b

• -4= -3 + b • -1 = b

• Y = -1/2 x – 1

Step 1: Find the slope.

Step 2. Substitute given x, y into the equation.

Step 3: Solve for b.

Step 4: Substitute m and b into the equation. Y = ___x + ___.

Example 2: Write the equation of the line that is perpendicular to y = -4/5x + 3 and

goes through the point (-8, 2)

• Step 1: Find the slope.

• Step 2. Substitute given x, y into the equation.

• Step 3: Solve for b.

• Step 4: Substitute m and b into the equation.

Y = ___x + ___..

Original m = -4/5, opposite reciprocal m = 5/4

2 = 5/4 ( -8) + b 2 = -10+ b 12 = b

Y = 5/4x + 12

Summary: • What is the difference between parallel

and perpendicular slopes when writing equations of lines?