What do I know? – Linear Models
Name: _________________________ Date ___________________________
1. From this graph:
6 y
5
a)
Complete this table-of-values.
4
3
x
0
1
2
3
2
1
y
x
−6
−5
−4
−3
−2
−1
1
2
3
4
5
6
−1
b) Determine the equation of the line
−2
−3
−4
−5
−6
2.
From this table-of-values:
x
y
-2
6
-1
4
0
2
8 y
1
0
2
-2
3
-4
6
4
a) Plot the graph on the number plane.
2
x
b) Determine the equation of the line.
−6
−4
−2
2
−2
−4
−6
−8
3. a) Determine if this table represents a linear relationship.
b) Explain your answer clearly.
x
y
1
7
2
3
3
-1
4
-5
5
-9
6
-13
4
6
4.
Sketch each line on a graph showing at least 2 points.
3
5
b) y = - x  2
a) y = 4x – 2
8 y
8 y
6

6
4
4
2
2
x
−6
−4
−2
2
4
6
x
−6
−4
−2
2
4
6
−2
−4
−4
−6
−6
−8
5.
−2
−8
Determine the equation of these lines.
b) with a slope of zero and a y-intercept of 5
y
x
c) with a slope of -2 passing through the point (-8,6)
d)
e) passing through the points (5, -1) and (4, 3)
f)
Passing through the point (4, 3) and parallel to the
line y = -x + 8
2x + 4y = 16, hence sketch on the number plane
6. Determine the slope and y-intercept of the line:
8 y
6
4
2
x
−6
−4
−2
2
4
6
−2
−4
−6
−8
7.
Find the equation of the line with a slope of -4 and passing through (1, 3). Represent the equation in standard form;
ax + by = c, where a, b ɛ Ζ
a)
8.
Determine the x and y intercept of this line, hence sketch the line on the number plane.
8 y
-3x + 2y = 12
6
4
2
x
−6
−4
−2
2
−2
−4
−6
−8
9.
What is the slope of a line that is perpendicular to the line y = 5x – 3?
4
6
10. A hot air balloon is coming into land from off from a spot 200 meters above the ground.
The balloon drops 25 meters every minute.
Which is the independent variable?
Which is the dependent variable?
Let x = _____________________
a)
Let_y = ________________________
Complete the table-of values below.
x
0
1
2
3
4
5
y
b)
Select one of the points in the table above and explain its meaning in the context of the problem.
c)
Plot the points from your table on the graph below. Make sure to label your axes with your answers from part ‘a’.
8
y
7
6
5
4
3
2
1
x
1
d)
e)
f)
2
3
4
5
6
Write an equation in x and y to model this situation. Remember what x and y represent.
Use your equation model to determine the height of the balloon after 3.2 minutes.
Use your equation model to determine how long it will take for the balloon to land on the ground?