March 29, 2017
Aim #5: How do we write equations of parallel and perpendicular lines? CC Geometry R
Do Now:
1. Complete:
a. If two lines are _____________, their slopes are equal.
b. If two lines are perpendicular, their slopes are__________ _________.
c. If two lines are perpendicular, the product of their slopes is ______.
2. ΔABC has vertices A(0,10), B(-8,8) and C(-3,5).
a. Determine if ΔABC is a right triangle.
A(0,10)
B(­8,8)
b. Write an equation of the line through B,
parallel to the y-axis.
C(­3,5)
c. Write an equation of the line through C,
perpendicular to the y-axis.
1. Determine whether the lines given by the equations 2x + 3y = 6 and
y = 3 x + 4 are perpendicular. Explain your answer.
2
2. Which line(s) are parallel to the line with equation 2y - 3x - 10 = 0?
(a) 3x - 2y = 8
(b) 12x + 8y = 0
(c) 4y = 6x
(d) ½y = ¾x - 2
3. Which line(s) are perpendicular to the line with equation 2y - 3x = 0?
(a) 6y = -4x
(b) y +
+1=0
(c) 6x = 8 - 9y (d) y =
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To write an equation of a line, use slope-intercept form.
SLOPE-INTERCEPT FORM
y = mx + b
The equations below are in standard form. Put each equation in slope-intercept
form. State the slope and y-intercept:
6x + 3y = 12
5x + 7y = 14
2x - 5y = 30
#1-5 Use the above results.
1. Write an equation of the line parallel to 6x + 3y = 12, passing through (0,-8).
2. Write an equation of the line perpendicular to 6x + 3y = 12, passing through (0,3.5).
3. Write an equation of the line parallel to 5x + 7y = 14, passing through (-14,1).
4. Write an equation of the line perpendicular to 2x - 5y = 30 , passing through
(-10,-4).
5. Write an equation of a line perpendicular to 5x + 7y = 14 with the same
y-intercept as 2x - 5y = 30.
6. Two perpendicular lines have the same y-intercept. If the equation of one of
these lines is y = - 4 x + 6, what is the equation of the other line?
5
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Exercises
1. Given the points R(2,2) and V(3,6), write the
equation of the line through R and perpendicular to RV.
2. Given U(-2,0) and V(4,3):
a. Write an equation for the line through U and
perpendicular to UV.
b. Write an equation for the line through V and
perpendicular to UV.
3. Given S(-2,7) and T(4, 4):
a. Write an equation for the line through
S and perpendicular to ST.
b. Write an equation for the line through
T and perpendicular to ST.
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4. Given A(-5, -3), B(-1, 6) and C(8,2):
a. Write an equation of line BC in slope-intercept
form.
B
6
4
C
2
­4
b. Determine if line AB
­2
0
0
2
4
6
8
line CB.
­2
A
5. Given the points C(-3,2) and D(4,4), write the equation of the line through C
and perpendicular to CD.
6. Given the points H(-2,-3) and Q(2,-1), write the equation of the line through Q
and perpendicular to HQ.
Let's Sum it Up!
Given slope m, y-intercept b, and point (x1,y1), the two forms of the equation of
a line are
• slope-intercept form:
y = mx + b
• point-slope form:
(y - y1) = m(x - x1)
A vertical line has undefined slope and is of the form x = c (c = constant).
A horizontal line has 0 slope and is of the y = c (c = constant).
Slopes of parallel lines are equal.
Slopes of perpendicular lines are opposite reciprocals.
March 29, 2017
Name_____________________________
C Geometry R
Date ____________________
HW #5
1. Are the lines parallel, perpendicular, or neither?
a. 3x + 2y = 74 and 9x - 6y = 15
b. 4x - 9y = 8 and 18x + 8y = 7
2. Given points C(-4,3) and D(3,3):
a. Write an equation of the line through
C and perpendicular to CD.
b. Write an equation of the line through
D and perpendicular to CD.
3a. Write an equation of a line through (0,-7) and parallel to the line y = 1 x + 5.
2
b. If a line is perpendicular to y =
1
x + 5, will it be perpendicular to x – 2y = 14?
2
4 a. Write an equation of the line passing through (-1,10)
parallel to the x-axis.
b. Write an equation of the line passing through (2.5,
perpendicular to the x-axis.
)
5. Find an equation of a line through (-5, 3) and:
a. parallel to x = –9
b. perpendicular to x = 4
c. parallel to y =
6. Write an equation of the line that passes through the origin that intersects
the line 2x + 5y = 7 to form a right angle.
OVER
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7. Write an equation of the line passing through (-3,4) and perpendicular to
the line with equation 2x + 7y = -3
8. A coach is laying out lanes for a race. The lanes are perpendicular to a segment
of the track such that one endpoint of the segment is (2,50) and the other is
(20,65). What are the equations of lines l and m through the endpoints?
(20,65)
(2,50)
m
l
Review:
1) The diagram below, a right circular cone with a radius of 3 inches has a slant
height of 5 inches, and a right cylinder with a radius of 4 inches has a height of
6 inches. Determine and state the number of full cones of water needed to
completely fill the cylinder with water.
2) The line y = 3x - 4 is dilated by a scale factor of 2. Which equation represents
the image of the line after the dilation?
a) y = 6x - 8
b) 2y = 6x - 8
c) y = 6x - 4
d) y = 3x - 8
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