Linear Law Questions: Math Quiz!

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Quizzes Created: 1 | Total Attempts: 178
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  • 1/10 Questions
    Two variables, x, and y are related by the equation  . Write down the y-intercept of the graph of y against .   - ProProfs

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

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About This Quiz

Engage with this interactive math quiz focused on linear laws, exploring relationships between variables, gradients, and intercepts in various mathematical contexts.

Linear Law Questions: Math Quiz! - Quiz

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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 .   - ProProfs

    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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  • 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. - ProProfs

    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. 
    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. - ProProfs

    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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  • 5. 
    Two positive variables, x and y are related by the equation  .Write down the y-intercept of the graph of  against . - ProProfs

    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 . - ProProfs

    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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  • 7. 
    Given the graph shown below, express y in terms of x. - ProProfs

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

    • Y = 0.5x^(0.5) + 4.5

    • Y = 0.5x + 4.5x^(0.5)

    • Y = 0.5x + 4.5

    • Y = 0.5x + 4.5x^2

    Correct Answer
    A. 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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  • 8. 
    The diagram shows a straight line graph obtained by plotting xy against x. Find y in terms of x. - ProProfs

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

    • Y = -0.5x + 3

    • Y = -0.5 + 3x

    • y = -0.5x + 13

    • Y = -0.5 + (3/x)

    Correct Answer
    A. 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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  • 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.

    • X = 2.16, x = -4.16

    • X = -2.16, x = 4.16

    • X = -7.19, x =-2.19

    • 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?

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

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

    Correct Answer
    A. 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
    Quiz Edited by
    ProProfs Editorial Team
  • Jul 13, 2009
    Quiz Created by
    Limhuangsf
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