Understanding Linear Equations
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Questions and Answers

What is a key characteristic of a linear equation?

  • Plotting as a straight line on a graph (correct)
  • Variables with exponents other than one
  • Representation as a curved line on a graph
  • Having more than two variables

    • In which form does a linear equation have parts including the slope and y-intercept?

  • Standard form
  • Point-slope form
  • Intercept form
  • Slope-intercept form (correct)

    • What does the y-intercept represent in a linear equation?

  • The variables of the equation
  • The place where the line crosses the y-axis (correct)
  • The slope of the line
  • The place where the line crosses the x-axis

    • If a linear equation has a slope of 0, what type of line does it represent on a graph?

    <p>A horizontal line</p> Signup and view all the answers

    How can a linear equation be written using the slope and intercept values?

    <p>Determining the slope and y-intercept</p> Signup and view all the answers

    What is the formula for a linear equation in the form y = mx + c?

    <p>y = 2x + 3</p> Signup and view all the answers

    When creating a linear equation from two points (1,1) and (3,2), what is the slope (m) calculated to be?

    <p>0.5</p> Signup and view all the answers

    For the linear equation y = 2x + c, if the point (1,1) is substituted, what is the value of c?

    <p>-1</p> Signup and view all the answers

    Which formula can be used to calculate the slope of perpendicular lines?

    <p>$m1 \times m2 = -1$</p> Signup and view all the answers

    In linear equations written as functions, what is another way to represent y = mx + c?

    <p>$f(x) = mx + c$</p> Signup and view all the answers

    What is the standard form of a linear equation?

    <p>$ax + by = c$</p> Signup and view all the answers

    If a linear equation has a slope (m) of 4 and crosses the y-axis at y = -3, what is the linear equation in slope-intercept form?

    <p>$y = 4x - 3$</p> Signup and view all the answers

    What is the x-intercept of the linear equation 3x - 2y = 6?

    <p>(2, 0)</p> Signup and view all the answers

    Which part of the linear equation $y = -5x + 2$ represents the slope?

    <p>-5</p> Signup and view all the answers

    Given a linear equation in point-slope form as $y - 3 = 2(x - 1)$, what is the y-value of the point it passes through?

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

    What is the formula for calculating the slope (m) of a linear equation given two points (x1, y1) and (x2, y2)?

    <p>$m = \dfrac{y2 - y1}{x2 - x1}$</p> Signup and view all the answers

    In the equation y = 2x + 3, what does the value of 3 represent?

    <p>Y-intercept (c)</p> Signup and view all the answers

    What is the equation for finding the y-intercept (c) in a linear equation given two points (x1, y1) and (x2, y2)?

    <p>$c = x1 + \left(\dfrac{x2 - x1}{y2 - y1}\right)y1$</p> Signup and view all the answers

    When creating a linear equation from two points, why is it important to be consistent with labeling them as (x1, y1) and (x2, y2)?

    <p>To avoid confusion and errors in calculations</p> Signup and view all the answers

    In the context of making linear equations more identifiable, what is the purpose of writing linear equations as functions such as f(x), g(x), h(x), etc.?

    <p>To help with identification when dealing with multiple lines</p> Signup and view all the answers

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