Question

year 9 (core) linear relationships topic test 2026

part a - multiple-choice questions (1 mark each)

1. what is the y-coordinate of the point (3, -4)?

a. 3
b. -4
c. 0
d. -3

1. which of the following equations represents a linear relationship?

a. y = 2x - 1
b. y = x^2 + 4
c. y = 3^x
d. y = 1/x^2

1. which equation describes a vertical line with an x-intercept of 5?

a. y = 5
b. x + y = 5
c. y = 5x
d. x = 5

1. if a line rises 6 units for every 2 units it runs to the right, what is its gradient (m)?

a. 2
b. 6
c. 3
d. 12

1. for the line with the equation y = -2x + 7, what is the y-intercept (b)?

a. -2
b. 0
c. -7
d. 7

part b - short-answer questions (1 mark each)

1. complete the table of values for the linear rule

a) y = 3x

x | -1 | 0 | 1 | 2
y | 12 | 3 | 4 | 5

b) y = -3x - 1

x | -1 | 0 | 1 | 2
y | -5 | -1 | -3 | -4

. determine if the point (2,8) lies on the following lies:
) y = 2x + 6
y = 3x + 2

for the linear relationship y = 2x + 8:
find the y-intercept by substituting x = 0
find the x-intercept by substituting y = 0

1. on a cartesian plane:

a) sketch the graph of the line y = 2x - 4.
b) write the x-intercept:
c) y-intercept:

Explanation:

Identify coordinates

Using the Coordinate Geometry knowledge point

$$ (x, y) = (3, -4) \implies y = -4 $$

Identify linear equation

Using the Linear Relationships knowledge point

$$ y = 2x - 1 \text{ is linear (degree 1)} $$

Find vertical line equation

Using the Vertical Lines knowledge point

$$ x = c \implies x = 5 $$

Calculate gradient

Using the Linear Relationships knowledge point

$$ m = \frac{\text{rise}}{\text{run}} = \frac{6}{2} = 3 $$

Identify y-intercept

Using the Linear Intercepts knowledge point

$$ y = -2x + 7 \implies b = 7 $$

Complete table for y = 3x

Using the Linear Relationships knowledge point

$$
LATEXBLOCK0
$$

Complete table for y = -3x - 1

Using the Linear Relationships knowledge point

$$
LATEXBLOCK1
$$

Verify point on line

Using the Linear Relationships knowledge point

$$
LATEXBLOCK2
$$

Find intercepts for y = 2x + 8

Using the Linear Intercepts knowledge point

$$
LATEXBLOCK3
$$

Sketch graph of y = 2x - 4

Using the Graphing Linear Equations knowledge point

$$
LATEXBLOCK4
$$

Answer:

Part A - Multiple-choice questions

Question 1

• (A) 3
• (B) -4 (Correct answer)
• (C) 0
• (D) -3

Question 2

• (A) \(y = 2x - 1\) (Correct answer)
• (B) \(y = x^2 + 4\)
• (C) \(y = 3^x\)
• (D) \(y = \frac{1}{x^2}\)

Question 3

• (A) \(y = 5\)
• (B) \(x + y = 5\)
• (C) \(y = 5x\)
• (D) \(x = 5\) (Correct answer)

Question 4

• (A) 2
• (B) 6
• (C) 3 (Correct answer)
• (D) 12

Question 5

• (A) -2
• (B) 0
• (C) -7
• (D) 7 (Correct answer)

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Part B - Short-answer questions

Question 1

a) For \(y = 3x\):

\(x\)	\(-1\)	\(0\)	\(1\)	\(2\)

b) For \(y = -3x - 1\):

\(x\)	\(-1\)	\(0\)	\(1\)	\(2\)

Question 2

• For \(y = 2x + 6\): Since \(2(2) + 6 = 10

eq 8\), the point \((2,8)\) does not lie on the line.

• For \(y = 3x + 2\): Since \(3(2) + 2 = 8\), the point \((2,8)\) does lie on the line.

Question 3

• \(y\)-intercept: \(8\)
• \(x\)-intercept: \(-4\)

Question 4

a) To sketch \(y = 2x - 4\), plot the \(y\)-intercept at \((0, -4)\) and the \(x\)-intercept at \((2, 0)\), then draw a straight line passing through both points.
b) \(x\)-intercept: \(2\)
c) \(y\)-intercept: \(-4\)