Gr 11 Math Ch 4: Equations of a Line
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Questions and Answers

What is the equation of a straight line in the two-point form?

  • y = mx + c
  • (y - y_1)/(x - x_1) = (y_2 - y_1)/(x_2 - x_1) (correct)
  • y - y_1 = (y_2 - y_1)/(x_2 - x_1)(x - x_1)
  • y - y_1 = m(x - x_1)

    • Which form of the straight line equation is used when the gradient and one point on the line are known?

  • Two-point form
  • Gradient-point form (correct)
  • Gradient-intercept form
  • Slope-intercept form

    • What is the value of c in the equation y = mx + c?

  • slope of the straight line
  • gradient of the straight line
  • y-intercept of the straight line (correct)
  • x-intercept of the straight line

    • What is the equation of a straight line in the gradient-point form?

    <p>y - y_1 = m(x - x_1)</p> Signup and view all the answers

    Which of the following is a summary of the key points of the straight line equation?

    <p>Two-point form: used when two points are known, Gradient-point form: used when the gradient and one point are known, Gradient-intercept form: used when the gradient and y-intercept are known</p> Signup and view all the answers

    How do you derive the gradient-point form of the straight line equation?

    <p>By substituting m = (y_2 - y_1)/(x_2 - x_1) into the two-point form</p> Signup and view all the answers

    What is the standard form of the straight line equation?

    <p>y = mx + c</p> Signup and view all the answers

    Which of the following is not a form of the straight line equation?

    <p>Circle form</p> Signup and view all the answers

    What is the main purpose of the two-point form of the straight line equation?

    <p>To find the equation of the line when two points are known</p> Signup and view all the answers

    What is the value of y when x is 0 in the gradient-intercept form?

    <p>c</p> Signup and view all the answers

    What is the definition of the constant c in the gradient-intercept form?

    <p>c = y_1 - mx_1</p> Signup and view all the answers

    How do you derive the gradient-intercept form from the gradient-point form?

    <p>By expanding the brackets and making y the subject of the formula</p> Signup and view all the answers

    What is the gradient of the line when the equation is in the gradient-point form?

    <p>m = (y_2 - y_1) / (x_2 - x_1)</p> Signup and view all the answers

    What is the formula for the gradient-point form of the straight line equation?

    <p>y - y_1 = m(x - x_1)</p> Signup and view all the answers

    What is the main difference between the gradient-point form and the two-point form?

    <p>The gradient-point form uses the gradient and one point, while the two-point form uses two points</p> Signup and view all the answers

    Which of the following is a common use of the two-point form?

    <p>Finding the equation of a line when two points are known</p> Signup and view all the answers

    If two points on a line are (3, 4) and (6, 7), what is the value of x1 in the two-point form of the equation?

    <p>3</p> Signup and view all the answers

    What is the value of m in the gradient-point form when the gradient is 2 and the point is (3, 5)?

    <p>2</p> Signup and view all the answers

    If the equation of a line is y = 2x + 3, what is the y-intercept?

    <p>3</p> Signup and view all the answers

    What is the purpose of deriving the gradient-intercept form from the gradient-point form?

    <p>To find the y-intercept of a line</p> Signup and view all the answers

    If the equation of a line is y - 2 = 3(x - 1), what is the value of the gradient?

    <p>3</p> Signup and view all the answers

    What is the relationship between the two-point form and the gradient-point form?

    <p>The two-point form is used when two points are known, and the gradient-point form is used when the gradient and a point are known</p> Signup and view all the answers

    What is the advantage of using the gradient-intercept form?

    <p>It allows us to easily find the y-intercept</p> Signup and view all the answers

    If the equation of a line is y = mx - 2, what is the value of the y-intercept?

    <p>-2</p> Signup and view all the answers

    What is the main advantage of using the gradient-intercept form over the two-point form?

    <p>It is easier to find the y-intercept of the line.</p> Signup and view all the answers

    Which of the following is NOT a step in deriving the gradient-intercept form from the gradient-point form?

    <p>Subtracting x from both sides of the equation.</p> Signup and view all the answers

    What is the primary purpose of the two-point form?

    <p>To find the equation of a line given two points.</p> Signup and view all the answers

    Which form of the straight line equation is most useful when the gradient and y-intercept are known?

    <p>Gradient-intercept form.</p> Signup and view all the answers

    What is the relationship between the gradient-point form and the two-point form?

    <p>They are equivalent forms.</p> Signup and view all the answers

    Which of the following is an example of a real-world application of the gradient-intercept form?

    <p>All of the above.</p> Signup and view all the answers

    What is the main difference between the gradient-intercept form and the two-point form?

    <p>The gradient-intercept form provides the y-intercept, while the two-point form does not.</p> Signup and view all the answers

    Which of the following is a limitation of the two-point form?

    <p>It requires two points on the line.</p> Signup and view all the answers

    What is the common requirement for using the two-point form and the gradient-point form of the straight line equation?

    <p>One point on the line is known.</p> Signup and view all the answers

    What is the purpose of defining the constant c in the gradient-intercept form of the straight line equation?

    <p>To represent the y-intercept of the line.</p> Signup and view all the answers

    When is the two-point form of the straight line equation more useful than the gradient-point form?

    <p>When two points on the line are known.</p> Signup and view all the answers

    What is the advantage of using the gradient-intercept form of the straight line equation?

    <p>It is easier to find the y-intercept of the line.</p> Signup and view all the answers

    What is a common situation in which the gradient-point form of the straight line equation is used?

    <p>When the gradient and one point on the line are known.</p> Signup and view all the answers

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