Linear Functions Practice Page 2
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2
31.3 – Linear Functions Practice Questions
1. Graph the following using the method of your choice.
2
3
= x
−
=
+
=
−
+
f
(
x
)
2
1
a)
b)
g
(
x
)
x
1
c)
h
(
x
)
x
3
3
5
=
2 −
=
15 −
=
d)
y
x
e)
y
x
30
f)
f
(
x
)
4
−
30
x
= x
−
=
+
=
2 −
f
(
x
)
4
50
g
(
x
)
20
x
g)
h)
i)
4
2. Find the slope given:
2
= x
+
=
−
−
a)
f
(
x
)
2
1
b)
g
(
x
)
x
3
3
c) points on line A(2,3) & B(-3,5)
d) points on line C(-3,4) & D(4,-5)
3. Find equation of lines given:
a) slope = 3 and y-intercept of -3
b) slope of -½ and point (3, -2)
c) slope of 4 and x-intercept of 4
d) through points A(2,5) and B(6,1)
e)
f)
4. What is the effect of changing the slope from 2 to 3 in a linear function?
5. What is the effect of changing the y-intercept from 30 to 40 in a linear function?
6. A submarine cruising at 30m below the surface starts to dive at a rate of 2 metres every 5
seconds.
a) Come up with an function to describe the submarine’s depth as a function of time.
b) Use your function to calculate the submarine’s depth after 2 minutes.
c) How long will it take the submarine to reach a depth of 138m?
2
2
9
=
=
−
=
−
m
m
m
Answers 2. a) m=2 b)
c)
d)
3. a) y=3x-3 b) 0=x-2y+1 c) y=4x-16 d) x+y-7=0
3
5
7
2
=
+
y
x
1
e)
f) x+3y+6 = 0 4. line gets steeper, y-intercept stays the same. 5. line moves up parallel to
3
2
=
−
−
d
) (
t
t
30
original (i.e. same slope) 6.a)
b) d=-78m c) t=270s or 4½ minutes
5
1.3 – linear functions
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