Question

year 9 (core) linear relationships
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 = \frac{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\\)

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

1. complete the table of values for the linear rule

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

Explanation:

Identify the y-coordinate of the point

For any ordered pair \((x, y)\), the first number represents the \(x\)-coordinate and the second number represents the \(y\)-coordinate.
Given the point \((3, -4)\):

• The \(x\)-coordinate is \(3\).
• The \(y\)-coordinate is \(-4\).

Determine the linear relationship

A linear relationship is represented by an equation of the form \(y = mx + c\), where the variables \(x\) and \(y\) are to the first power.

• Option A: \(y = 2x - 1\) is in the form \(y = mx + c\). This is linear.
• Option B: \(y = x^2 + 4\) contains \(x^2\), which is quadratic.
• Option C: \(y = 3^x\) contains \(x\) in the exponent, which is exponential.
• Option D: \(y = \frac{1}{x^2}\) contains \(x\) in the denominator with power \(2\), which is non-linear.

Identify the vertical line equation

A vertical line has a constant \(x\)-value for all points on the line. Its equation is always in the form \(x = k\), where \(k\) is the \(x\)-intercept.

• The question asks for a vertical line with an \(x\)-intercept of \(5\).
• This corresponds to the equation \(x = 5\).

Complete the table of values

The given linear rule is \(y = 3x\). We substitute each given \(x\)-value into the rule to find the corresponding \(y\)-value:

• For \(x = -1\):

$$y = 3(-1) = -3$$

• For \(x = 0\):

$$y = 3(0) = 0$$

• For \(x = 1\):

$$y = 3(1) = 3$$

Answer:

Part A - Question 1

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

Part A - Question 2

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

Part A - Question 3

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

Part B - Question 1

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