Post on 11-Dec-2021
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).