Name _______________________________________________ Date ________ Lesson 4.3 – Writing Equations of Parallel and Perpendicular Lines CC Geometry Do Now Find the slope and y-intercept of the following:

a) y – 4 = 3x b) y – 3x = 4 c) 8 – 2y = 6

Slope Activity 1. Use the following equations for question 1.

62 � xy 62 � xy 42 � xy

a) find the slope of each (m) b) find the y-intercept of each (b) c) graph the three equations on the same set of axes (below)

Questions: 1. What observations can you make about the three lines? 2. What do you notice about the slope (m) of each of the

lines?

3. Draw a conclusion based on this activity:

They all have the same slope

When lines have the same slope they are parallel

The lines do not intersect and they have the same slope

Answer key

2. Use the following equations for question 2

423

� xy 132

�� xy

a) find the slope of each (m) b) find the y-intercept of each (b) c) graph each on the same set of axes

Questions: Use the protractor provided to measure the angle formed by the two lines then answer the following questions: 1. What was the measure of the angle created?

2. What observations did you make about the lines?

3. Can you find any connections between the slopes of the two lines? Explain.

4. Draw a conclusion based on this activity.

x Parallel Lines have __________________________________________.

x Perpendicular Lines have ______________________________________________.

90 degrees

The lines are perpendicular

The slops are negative reciprocal of one another

When the slopes ate negative reciprocal, the lines are perpendicular

Negative reciprocal slopes

the same slope

1. Write the equation of a line that is parallel to the line y = -2x + 4 and passes through the point (-3, 5). 2. Write the equation of a line that is perpendicular to the line y = -3x + 4 and passes through the point

(-3, 9). 3. Write the equation of a line that is perpendicular to the line 3y = -15x – 12 and passes through the

point (-15, 5). 4. Write the equation of a line that is parallel to the line 8 + 3y = x – 4 and passes through the point

(-6, 8).

5. Write the equation of the line parallel to the x-axis which passes through the point (2, 4). 6. Write the equation of the line parallel to the y-axis which passes through the point (2, 4).

7. Given the following equations of lines, determine whether the lines are parallel, perpendicular or neither.

a) 1474

� �

xyxy

b) 4

6� ��

xyxy

c) 1

23

632

�

�

xy

xy

d) 141082

� �

yxxy

e) xy

xy9183

93 ��

� f)

7235.�� �

yxxy

8. Write the equation of a line that is parallel to the line 82 � yx and passes through the point (9, -3). 9. Write the equation of a line that is perpendicular to the line yx 963 �� and passes through the point

(3, -5).

10. Write the equation of a line that is parallel to the line 232

� yx and passes through the point

(12, -1).

11. Write the equation of a line that is perpendicular to the line 343

�� yx and passes through the point

(0, 5).