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Lines quiz

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  • How is the slope of a line calculated using two points?
    The slope is calculated as (y2 - y1) / (x2 - x1), representing the change in y divided by the change in x.
  • What does the Greek letter delta (Δ) represent in the slope formula?
    Delta represents the change in a variable; Δy is the rise and Δx is the run.
  • What does a positive slope indicate about the direction of a line?
    A positive slope means the line rises from left to right.
  • What does a negative slope indicate about the direction of a line?
    A negative slope means the line falls from left to right.
  • What is the slope of a perfectly horizontal line?
    The slope of a horizontal line is 0 because there is no change in y.
  • What is the slope of a perfectly vertical line?
    The slope of a vertical line is undefined because the change in x is 0, which cannot be divided.
  • What is the slope-intercept form of a line and what do its variables represent?
    The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.
  • How do you graph a line given in slope-intercept form?
    First plot the y-intercept, then use the slope to find another point, and connect the points with a line.
  • What is the point-slope form of a line and when is it used?
    Point-slope form is y - y1 = m(x - x1), used when you know the slope and a point the line passes through.
  • How do you convert a line from standard form to slope-intercept form?
    Solve for y to isolate it on one side, then rewrite the equation as y = mx + b.
  • What is the key characteristic of parallel lines regarding their slopes?
    Parallel lines have equal slopes but different y-intercepts.
  • How are the slopes of perpendicular lines related?
    Perpendicular lines have slopes that are negative reciprocals of each other.
  • How do you find the equation of a line given a slope and a point?
    Use the point-slope form, plugging in the slope and the coordinates of the given point.
  • How do you find the x-intercept and y-intercept from a line in standard form?
    Set y = 0 to solve for the x-intercept, and set x = 0 to solve for the y-intercept.
  • What equation describes a horizontal line and a vertical line?
    A horizontal line is y = b (where b is a constant), and a vertical line is x = a (where a is a constant).