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Slope of Linear Graphs quiz #1

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  • How do you determine the slope of a line on a graph?
    To find the slope, select two points on the line that intersect grid lines, calculate the vertical change (rise) and horizontal change (run), then divide rise by run using the formula (Y2 - Y1) / (X2 - X1).
  • What is the slope of a line that is perpendicular to a given line on a graph?
    The slope of a perpendicular line is the negative reciprocal of the original line's slope. For example, if the original slope is m, the perpendicular slope is -1/m.
  • What is the slope of a line that is perpendicular to the line x = -3?
    The line x = -3 is vertical and has an undefined slope. A line perpendicular to it is horizontal and has a slope of 0.
  • How do you find the slope of line p on a graph?
    To find the slope of line p, choose two points on line p that intersect grid lines, calculate the rise (change in y) and run (change in x), and divide rise by run.
  • How do you find the slope from a table of values?
    To find the slope from a table, select two pairs of (x, y) values, calculate the change in y divided by the change in x: (Y2 - Y1) / (X2 - X1).
  • What does a negative slope indicate about the direction of a line on a graph?
    A negative slope means the line goes downhill from left to right, showing a downward trend.
  • How does the steepness of a line relate to the numerical value of its slope?
    The larger the absolute value of the slope, the steeper the line; smaller values indicate a gentler slope.
  • When calculating slope, what sign is assigned to movement upward and to the right on a graph?
    Movement upward and to the right is assigned a positive sign for both rise and run.
  • If a line moves from a y-value of 4 to 6 and an x-value of 3 to 4, what is the slope?
    The slope is (6 - 4) / (4 - 3) = 2 / 1 = 2.
  • Why is it helpful to choose points that intersect grid lines when calculating slope on a graph?
    Choosing points that intersect grid lines makes it easier to read exact coordinates and calculate rise and run accurately.