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!

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| By Limhuangsf

Limhuangsf

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Quizzes Created: 1 | Total Attempts: 165

Questions: 10 | Attempts: 165 | Updated: Mar 19, 2023

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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)

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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.

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4
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

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4
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)

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4
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)

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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)

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4
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

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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)

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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

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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.

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Current Version
Mar 19, 2023

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Jul 13, 2009

Quiz Created by
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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?