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Middle Years

10.06 The point of intersection

Worksheet
Points of intersection
1

For each of the following, state the coordinates of the point of intersection of the two lines:

a
-5
-4
-3
-2
-1
1
2
3
4
5
6
7
x
-5
-4
-3
-2
-1
1
2
3
4
5
6
7
y
b
-4
-3
-2
-1
1
2
3
4
x
-4
-3
-2
-1
1
2
3
4
y
c
-7
-6
-5
-4
-3
-2
-1
1
2
x
-8
-7
-6
-5
-4
-3
-2
-1
1
2
y
d
-2
-1
1
2
3
4
5
6
7
8
x
-2
-1
1
2
3
4
5
6
7
8
9
y
e
-2
-1
1
2
3
4
5
6
x
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
1
y
f
-2
-1
1
2
3
4
5
6
7
8
9
x
-2
-1
1
2
3
4
5
6
7
8
9
y
g
-3
-2
-1
1
2
3
4
5
6
7
8
x
-9
-8
-7
-6
-5
-4
-3
-2
-1
1
2
y
h
-8
-7
-6
-5
-4
-3
-2
-1
1
2
x
-8
-7
-6
-5
-4
-3
-2
-1
1
2
y
i
-4
-3
-2
-1
1
2
3
4
x
-2
-1
1
2
3
4
5
6
7
y
j
-1
1
2
3
4
5
6
7
8
9
10
11
x
-4
-3
-2
-1
1
2
3
4
5
6
y
2

The graph of y = 3 x - 4 is shown on the coordinate plane:

a

Consider the horizontal line with equation y = 8.

State the point of intersection of the graph of y = 3 x - 4 with the line y = 8.

b

Hence determine the value of x that solves the equation 3 x - 4 = 8.

-4
-3
-2
-1
1
2
3
4
x
-2
-1
1
2
3
4
5
6
7
8
9
y
3

The graph of y = -2 x - 4 is shown on the coordinate plane:

a

State the point of intersection of the graph with the line y = - 12.

b

Hence determine the value of x that solves the equation - 2 x - 4 = - 12.

-5
-4
-3
-2
-1
1
2
3
4
5
6
x
-14
-12
-10
-8
-6
-4
-2
2
y
4

The graph of y = -\dfrac{x}{2} + 6 is shown on the coordinate plane:

a

In order to solve the equation \\- \dfrac{x}{2} + 6 = 8, state the equation of the other line that must be graphed on the axes.

b

Hence find the solution to - \dfrac{x}{2} + 6 = 8.

c

Explain why it is not necessary to write the y-value in your answer to part (b).

-6
-5
-4
-3
-2
-1
1
2
3
x
-1
1
2
3
4
5
6
7
8
9
10
y
5

The graph of y = \dfrac{4x}{3} + 5 is shown on the coordinate plane:

a

In order to solve the equation \\ \dfrac{4x}{3} + 5 = 13, state the equation of the other line that must be graphed on the axes.

b

Hence find the solution to \dfrac{4 x}{3} + 5 = 13.

-4
-3
-2
-1
1
2
3
4
5
6
7
x
-1
1
2
3
4
5
6
7
8
9
10
11
12
13
y
6

Emma wishes to find the point of intersection of the following lines:

y = -2 x + 3 \\ y = -1
a

Complete the table of values for \\y = -2 x + 3:

x-101
y
b

Sketch the graphs of both lines on a coordinate plane.

c

Hence determine the point of intersection.

7

Scott wishes to find the point of intersection of the following lines:

y = 2 x + 1 \\ y = -3 x + 11
a

Complete the table of values for \\y = 2 x + 1:

x-101
y
b

Complete the table of values for \\y = -3 x + 11:

x-101
y
c

Sketch the graphs of both lines on a coordinate plane.

d

Hence determine the point of intersection.

8

For each of the following pairs of equations:

i

Sketch the graph of the two lines on the same coordinate plane.

ii

Find the coordinates of the point of intersection.

a

y = 3

x = - 3

b

y = 2 x + 2

x = - 3

c

y = 3 x - 4

y = 5

d

y = - 2 x + 4

y = 8

e

y = 3 x + 3

x = - 1

f

y = x + 3

y = 3 x - 5

g

y = - x + 6

y = x + 2

h

y = - x + 2

y = 2 x - 4

i

y = - 4 x + 2

y = 3 x - 12

j

y = \dfrac{x}{2} + 3

y = 3 x - 2

k

y = \dfrac{x}{2} - 2

y = - 2 x + 3

l

y = 5 x + 6

y = 2 x + 12

m

y = 3 x - 3

y = - 4 x + 11

n

y = x - 9

y = - x - 7

o

y = 2 x - 7

y = - \dfrac{x}{2} - 2

p

y = \dfrac{x}{2} + 5

y = 3 x

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