It is known that x and y are related by the equation ay = bx3 - x, where a and b are unknown constants. Express this equation in a form suitable for drawing a straight-line graph, and state which variable should be used for each axis. Which of the following statement is correct?

Plot (y/x) against ($$x^2)$$, gradient = (b/a) and (y/x)-intercept = -(1/a)

Plot (y/x) against ($$x^2)$$, gradient = (b/a) and y-intercept = -(1/a)

Plot (y/x) against (x), gradient = (-b/a) and y-intercept = -(1/a)

Plot (y/x) against (x), gradient = (-b/a) and (y/x)-intercept = -(1/a)

Linear Law Questions: Math Quiz!

Approved & Edited by ProProfs Editorial Team

The ProProfs editorial team is comprised of experienced subject matter experts. They've collectively created over 10,000 quizzes and lessons, serving over 100 million users. Our team includes in-house content moderators and subject matter experts, as well as a global network of rigorously trained contributors. All adhere to our comprehensive editorial guidelines, ensuring the delivery of high-quality content.

Learn about Our Editorial Process

| By Limhuangsf

Limhuangsf

Community Contributor

Quizzes Created: 1 | Total Attempts: 175

Questions: 10 | Attempts: 175 | Updated: Mar 19, 2023

Quiz Flashcard

Questions

Settings

Feedback

During the Quiz End of Quiz

Difficulty

Sequential Easy First Hard First

Create your own Quiz

Share on Facebook Share on Twitter Share on Whatsapp Share on Pinterest Share on Email Copy to Clipboard Embed on your website

Questions and Answers

1.

Two variables, x, and y are related by the equation . Write down the y-intercept of the graph of y against .

Explanation
The equation can be expressed as y = 3(1/x) + 5, which is of the form Y = mX + c where Y = y, X = (1/x)

Rate this question:

1
2.

Two variables, x and y are related by the equation . Write down the gradient of the graph of xy against .

Explanation
The gradient of the graph of xy against x is -3. This means that for every unit increase in x, the value of xy decreases by 3. In other words, the graph has a negative slope of -3.

Rate this question:
3.

Two variables, x and y are related by the equation . Write down the gradient of the graph of lg y against x to 3 significant figures.

Explanation
Taking lg to both sides of the equation, we get
lg(y) = lg3 - xlg4 which is of the form Y = mX + c where Y = lg(y), X = x

Rate this question:
4.

Two variables, x and y are related by the equation . Write down the y-intercept of the graph of lg y against lg x to 3 significant figures.

Explanation
Taking lg to both sides of the equation, we get
2lg(y) + 2lg(x) = lg5. Rearranging, we get lg(y) = -lg(x) + (lg5)/2 which is of the form Y = mX + c where Y = lg(y), X = lg(x)

Rate this question:
5.

Two positive variables, x and y are related by the equation .Write down the y-intercept of the graph of against .

Explanation
Dividing the equation throughout by x, we get y^2 = 2/(x^2)-3 which is of the form Y = mX + c where Y = y^2, X = 1/(x^2)

Rate this question:
6.

Two positive variables, x and y are related by the equation .Write down the gradient of the graph of against .

Explanation
Dividing both sides of the equation by xy, we get 1/y + 6/x = 2. Rearranging, we get 1/y = -6/x + 2 which is of the form Y = mX + c where Y = 1/y, X = 1/(x)

Rate this question:
7.

The diagram shows a straight line graph obtained by plotting xy against x. Find y in terms of x.
- A.
  
  Y = -0.5x + 3
- B.
  
  Y = -0.5 + 3x
- C.
  
  y = -0.5x + 13
- D.
  
  Y = -0.5 + (3/x)
Correct Answer
D. Y = -0.5 + (3/x)

Explanation
Let Y = mX + c ---- (1)
m = (8-2)/(-10-2) = -0.5
Subst (2,2) into (1), we get c = 3
Thus xy = -0.5x + 3. Expressing y in terms of x, we get y = -0.5 + 3/x

Rate this question:
8.

Given the graph shown below, express y in terms of x.
- A.
  
  Y = 0.5x^(0.5) + 4.5
- B.
  
  Y = 0.5x + 4.5x^(0.5)
- C.
  
  Y = 0.5x + 4.5
- D.
  
  Y = 0.5x + 4.5x^2
Correct Answer
B. Y = 0.5x + 4.5x^(0.5)

Explanation
Let Y = mX + c ---- (1)
m = (8-5)/(7-1) = 0.5
Subst (1,5) into (1), we get c = 4.5
Thus y/(x^0.5) = 0.5(x^0.5) + 4.5. Expressing y in terms of x, we get y = 0.5x + 4.5(x^0.5)

Rate this question:
9.

The variables x and y are related in such a way that when (y - x) is plotted against x², a straight line which passes (1,1) and (5, 3) is obtained. Find the values of x when y = 5.
- A.
  
  X = 2.16, x = -4.16
- B.
  
  X = -2.16, x = 4.16
- C.
  
  X = -7.19, x =-2.19
- D.
  
  X = 7.19, x = 2.19
Correct Answer
A. X = 2.16, x = -4.16

Explanation
Let Y = mX + c ---- (1)
m = (3-1)/(5-1) = 0.5
Subst (1,1) into (1), we get c = 0.5
Thus y-x = 0.5(x^2) + 0.5
When y = 5, 5-x = 0.5x^2+0.5. Simplifying, we get 0.5x^2+x-4.5 = 0. Solve for x to get x = 2.16, x = -4.16

Rate this question:
10.

It is known that x and y are related by the equation ay = bx³ - x, where a and b are unknown constants. Express this equation in a form suitable for drawing a straight-line graph, and state which variable should be used for each axis. Which of the following statement is correct?
- A.
  
  Plot (y/x) against (x^2), gradient = (b/a) and y-intercept = -(1/a)
- B.
  
  Plot (y/x) against (x^2), gradient = (b/a) and (y/x)-intercept = -(1/a)
- C.
  
  Plot (y/x) against (x), gradient = (-b/a) and y-intercept = -(1/a)
- D.
  
  Plot (y/x) against (x), gradient = (-b/a) and (y/x)-intercept = -(1/a)
Correct Answer
B. Plot (y/x) against (x^2), gradient = (b/a) and (y/x)-intercept = -(1/a)

Explanation
Divide the given equation by ax gives y/x = (b/a)x^2 - 1/a, which is of the form Y = mX + c where Y = y/x, X = x^2. When referring to the Y-intercept of this graph, we should call it the (y/x)-intercept and not y-intercept.

Rate this question:

Quiz Review Timeline +

Our quizzes are rigorously reviewed, monitored and continuously updated by our expert board to maintain accuracy, relevance, and timeliness.

Current Version
Mar 19, 2023

Quiz Edited by
ProProfs Editorial Team
Jul 13, 2009

Quiz Created by
Limhuangsf

Linear Law Questions: Math Quiz!

Two variables, x, and y are related by the equation . Write down the y-intercept of the graph of y against .

Two variables, x and y are related by the equation . Write down the gradient of the graph of xy against .

Two variables, x and y are related by the equation . Write down the gradient of the graph of lg y against x to 3 significant figures.

Two variables, x and y are related by the equation . Write down the y-intercept of the graph of lg y against lg x to 3 significant figures.

Two positive variables, x and y are related by the equation .Write down the y-intercept of the graph of against .

Two positive variables, x and y are related by the equation .Write down the gradient of the graph of against .

The diagram shows a straight line graph obtained by plotting xy against x. Find y in terms of x.

Given the graph shown below, express y in terms of x.

The variables x and y are related in such a way that when (y - x) is plotted against x2, a straight line which passes (1,1) and (5, 3) is obtained. Find the values of x when y = 5.

It is known that x and y are related by the equation ay = bx3 - x, where a and b are unknown constants. Express this equation in a form suitable for drawing a straight-line graph, and state which variable should be used for each axis. Which of the following statement is correct?

The variables x and y are related in such a way that when (y - x) is plotted against x², a straight line which passes (1,1) and (5, 3) is obtained. Find the values of x when y = 5.

It is known that x and y are related by the equation ay = bx³ - x, where a and b are unknown constants. Express this equation in a form suitable for drawing a straight-line graph, and state which variable should be used for each axis. Which of the following statement is correct?