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

2. which of the following equations represents a linear relationship?
a. $y = 2x - 1$
b. $y = x^2 + 4$
c. $y = 3^x$
d. $y = \frac{1}{x^2}$

3. which equation describes a vertical line with an x-intercept of 5?
a. $y = 5$
b. $x + y = 5$
c. $y = 5x$
d. $x = 5$

4. 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

5. 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) $y = 3x$
\begin{array}{|c|c|c|c|c|}
\hline
x & -1 & 0 & 1 & 2 \\
\hline
y & & & & \\
\hline
\end{array}

b) $y = -3x - 1$
\begin{array}{|c|c|c|c|c|}
\hline
x & -1 & 0 & 1 & 2 \\
\hline
y & & & & \\
\hline
\end{array}

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

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

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

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

2. which of the following equations represents a linear relationship?
a. $y = 2x - 1$
b. $y = x^2 + 4$
c. $y = 3^x$
d. $y = \frac{1}{x^2}$

3. which equation describes a vertical line with an x-intercept of 5?
a. $y = 5$
b. $x + y = 5$
c. $y = 5x$
d. $x = 5$

4. 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

5. 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) $y = 3x$
\begin{array}{|c|c|c|c|c|}
\hline
x & -1 & 0 & 1 & 2 \\
\hline
y & & & & \\
\hline
\end{array}

b) $y = -3x - 1$
\begin{array}{|c|c|c|c|c|}
\hline
x & -1 & 0 & 1 & 2 \\
\hline
y & & & & \\
\hline
\end{array}

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

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

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

Accepted Answer

{ "quality": "clear", "question_count": 5, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Linear Relationships", "Coordinate Geometry", "Vertical Lines" ], "current_concepts": [ "Coordinate Geometry", "Linear Relationships", "Vertical Lines", "Linear Intercepts" ] } ## Identify the y-coordinate of the point (3, -4) $$ \begin{aligned} &\text{Point: } (x, y) = (3, -4)\ &y = -4 \end{aligned} $$ ## Identify the linear relationship equation $$ \begin{aligned} &\text{Linear form: } y = mx + c\ &y = 2x - 1 \quad (\text{degree } 1) \end{aligned} $$ ## Determine the equation of the vertical line $$ \begin{aligned} &\text{Vertical line form: } x = k\ &x\text{-intercept} = 5 \implies x = 5 \end{aligned} $$ ## Calculate the gradient (m) $$ \begin{aligned} &m = \frac{\text{rise}}{\text{run}} = \frac{6}{2} = 3 \end{aligned} $$ ## Find the y-intercept (b) of the line y = -2x + 7 $$ \begin{aligned} &y = mx + b \implies y = -2x + 7\ &b = 7 \end{aligned} $$ ## Question 1 (A) 3

(B) -4

(C) 0

(D) -3 ## Question 2 (A) $y = 2x - 1$

(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) $x = 5$ ## Question 4 (A) 2

(B) 6

(C) 3

(D) 12 ## Question 5 (A) -2

(B) 0

(C) -7

(D) 7

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Coordinate Geometry" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Identify the y-coordinate of the point (3, -4)

Identify the linear relationship equation

Determine the equation of the vertical line

Calculate the gradient (m)

Find the y-intercept (b) of the line y = -2x + 7

Answer:

Question 1

Question 2

Question 3

Question 4

Question 5