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Slope-Intercept Form quiz

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  • What is the slope-intercept form of a linear equation?
    The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.
  • In the equation y = mx + b, what does the 'm' represent?
    The 'm' represents the slope of the line, which is the rise over run or the change in y divided by the change in x.
  • What does the 'b' represent in the equation y = mx + b?
    The 'b' is the y-intercept, which is the point where the line crosses the y-axis (when x = 0).
  • How do you find the slope from a graph?
    You find the slope by calculating the rise over run between two points on the line.
  • If a line has a slope of 2 and a y-intercept of 3, what is its equation in slope-intercept form?
    The equation is y = 2x + 3.
  • How do you determine the y-intercept from a graph?
    Look for the point where the line crosses the y-axis; the y-coordinate of this point is the y-intercept.
  • What is the point-slope form of a linear equation?
    The point-slope form is y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is a point on the line.
  • When should you use point-slope form instead of slope-intercept form?
    Use point-slope form when you are given the slope and a point that is not the y-intercept.
  • How can you convert an equation from point-slope form to slope-intercept form?
    Distribute the slope, simplify, and solve for y to get the equation in the form y = mx + b.
  • What is the relationship between the slopes of parallel lines?
    Parallel lines have the same slope but different y-intercepts.
  • What is the relationship between the slopes of perpendicular lines?
    Perpendicular lines have slopes that are negative reciprocals of each other.
  • If one line has a slope of 3/2, what is the slope of a line perpendicular to it?
    The perpendicular slope is -2/3, the negative reciprocal of 3/2.
  • How do you determine if two lines are parallel by looking at their equations in slope-intercept form?
    If the slopes (m values) are equal and the y-intercepts (b values) are different, the lines are parallel.
  • How do you determine if two lines are perpendicular by looking at their slopes?
    If the product of their slopes is -1, the lines are perpendicular.
  • Given the equation y = 1/3x + 2 and y = -3x + 6, are the lines parallel, perpendicular, or neither?
    They are perpendicular because their slopes (1/3 and -3) are negative reciprocals.