Linear Graphs and Slope Calculation
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Questions and Answers

What is the slope of a line passing through the points (4, 8) and (2, 4)?

  • 3
  • 0
  • 2 (correct)
  • 4
  • What is the equation of a line with a slope of -3 that intersects the y-axis at 5?

  • y = -3x - 5
  • y = -3x + 5 (correct)
  • y = -x - 5
  • y = 3x + 5
  • Given the equation y = 2x + 1, what is the y-intercept of the line?

  • 1 (correct)
  • 0
  • 3
  • 2
  • If the slope of a line is positive, which statement is true?

    <p>The line rises as it moves from left to right.</p> Signup and view all the answers

    In graphing the line represented by y = 1/2x + 4, where would the y-intercept be located?

    <p>4</p> Signup and view all the answers

    Study Notes

    Linear Graphs

    • A linear graph demonstrates a straight line, representing a consistent relationship between two variables.
    • The slope, or gradient, determines the steepness of the line. A positive slope indicates an upward trend; a negative slope indicates a downward trend.
    • The slope is calculated as the change in the y-axis divided by the change in the x-axis (rise over run).
    • The y-intercept is the point where the line crosses the y-axis. It represents the value of y when x is 0.
    • The equation of a straight line is represented as y = mx + b where m is the slope and b is the y-intercept.

    Finding Slope

    • The slope of a line passing through two points can be calculated using the formula: m = (y2 - y1) / (x2 - x1).

    Graphing a Line

    • To graph a line, start by plotting the y-intercept (the point where the line crosses the y-axis).
    • Use the slope to locate additional points. For instance, a slope of 2 indicates that for every increase of 1 on the x-axis, there is a corresponding increase of 2 on the y-axis.
    • Draw a straight line through all these points.
    • Remember to label the axes clearly and ensure they are scaled appropriately.

    Graph Reading Skills

    • To analyze a graph, observe the slope: if the line goes uphill, the slope is positive; if it goes downhill, the slope is negative.
    • Identify the intercepts, where the line crosses the x and y axes.
    • Use the graph to estimate values: for example, locate a point on the x-axis and estimate the corresponding y-value by tracing a vertical line to intersect with the line on the graph.

    Common Mistakes

    • Ensure that the x and y axes are clearly labeled, and the scaling is chosen to effectively display the data.
    • Understand that a positive slope indicates an upward trend.
    • When calculating the slope, simplify fractions to ensure accuracy.
    • Use online graphing tools, video tutorials, and practice worksheets to reinforce understanding and improve application.

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    Description

    This quiz covers the fundamentals of linear graphs, including the definition of slope, y-intercept, and the equation of a straight line. You'll learn how to calculate the slope between two points and how to graph a line using these concepts. Test your understanding of linear relationships and their graphical representation.

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