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Assignment 3.5
Math 10H
Slope ~ y intercept form: y  mx  b
General form: Ax  By  C  0
Slope ~ Point form: y  y1  m  x  x1 
1. Write the point-slope form of the equation of the line through the given point with the
given slope.
a) through (-5, 2), slope = -4
c) through (0, 9), slope =
1
4
e) through (-1, -6), slope = 0
b) through (-4, 7), slope = 2
d) through (5, 0), slope = 
f) through (8, -22), slope = 
2. Write the point-slope form of the equation of the line described below.
2
a) through (-3, 4), and parallel to y   x  1
3
b) through (-2, 5), and parallel to 3x  4y  8
c) through (10, -10), and parallel to the x -axis.
d) through (7, -3), and perpendicular to the x -axis.
e) through (-2 , -5), and perpendicular to y  3 x  9 .
5
3
3. Write the point-slope form of the equation of the line through the given points.
a) through (-5, -1) and (0, -1)
b) through (5, -2) and (8, 1)
c) through (2, -5) and (-8, -8)
d) through (2, -6) and (-4, 9)
4. Draw the graph of the linear function described in these slope-point equations.
y  1  3  x  5
a)
3
 x  2
4
Slope: ______ Point: _______
b) y  2 
Slope: ______
Point: _______
y
y
8
8
6
6
4
4
2
2
x
-8
-6
-4
-2
2
4
6
8
-6
-4
-2
2
-2
-2
-4
-4
-6
-6
-8
-8
y  4    x  4
c)
x
-8
Slope: ______
4
6
8
1
 x  2
2
Slope: ______ Point: _______
d) y  6  
Point: _______
y
y
8
8
6
6
4
4
2
2
x
-8
-6
-4
-2
2
4
6
8
x
-8
-6
-4
-2
2
-2
-2
-4
-4
-6
-6
-8
-8
4
6
8
5. Change from point-slope to slope y-intercept:
a)
y7 
1
 x  1
5
b) y  3  
3
 x  6
2
6. Change from point-slope to general form:
a)
y 11  5  x  3
b) y  8 
2
 x  10 
7
7. Write an equation, in slope-point form, for the line in each graph below. Use the
indicate point.
a)
b)
y
(-4,3)
y
4
4
2
2
x
-4
-2
2
4
-2
-4
_____________________
x
-4
-2
2
-2
(1, -3)
(1, -3)
-4
_____________________
4
8.
Two perpendicular lines intersect at point K (-2, -5). One line has equation
5
25
y   x  . What is the equation (in slope-point form) of the other line?
3
3
9.
Two perpendicular lines intersect on the y -axis. One line has equation
2
y  3   x  5  . What is the equation of the other line, in slope y-intercept form?
9
10. Two perpendicular lines intersect at M (3, 5). What might their equations be? Use
m as the slope for one of the lines.
How many possible pairs of equations are there?
Solutions to Assignment 3.5
1.
a) y  2  4  x  5
b)
y  7  2  x  4
d)
x 5
f)
y  22  
b)
y5 
c) y  10
1
e) y  5   x  2 
3
d)
x 7
a) y  1
b)
c) y  9 
1
x
4
e) y  6
2.
3.
a) y  4  
2
 x  3
3
3
 x  2  or
10
c)
3
y  8   x  8
10
d)
a) Slope: 3, Point: (-5, 1)
b)
3
 x  2
4
y  1   x  8  or
y  2   x  5
5
 x  2  or
2
5
y  9    x  4
2
3
Slope: , Point: (2, -2)
4
y5
4.
5
 x  8
3
y6  
y
y
8
8
6
6
4
4
2
2
x
x
-8
-6
-4
-2
2
4
6
-8
8
-6
-4
-2
2
-2
-2
-4
-4
-6
-6
-8
-8
c) Slope: -1, Point: (4, -4)
4
6
8
1
Slope:  , Point: (-2, 6)
2
d)
y
y
8
8
6
6
4
4
2
2
x
-8
-6
-4
-2
2
4
6
x
8
-8
-6
-4
-2
2
-2
-2
-4
-4
-6
-6
-8
-8
4
6
8
5.
6.
7.
8.
9.
10.
1
34
a) y  x 
5
5
a) 5x  y  4  0
1
a) y  3    x  4 
3
3
y  5   x  2
5
9
37
y x
2
9
b)
b)
b)
3
y   x6
2
2x  7y  76  0
5
y  3   x  1
2
1
 x  3
m
There are an infinite number of possible pairs of equations.
y  5  m  x  3 and y  5  