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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?
    '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?
    'b' is the y-intercept, 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 crosses the y-axis at -3, what is the value of b in its equation?
    The value of b is -3, since that's the y-intercept.
  • How do you write the equation of a line with slope 2 and y-intercept 3 in slope-intercept form?
    The equation is y = 2x + 3.
  • What is the point-slope form of a line?
    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 know 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 it into y = mx + b form.
  • 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, perpendicular, or neither using their equations?
    Put both equations in slope-intercept form and compare their slopes: same slopes mean parallel, negative reciprocals mean perpendicular, otherwise neither.
  • If a line has the equation y = x - 3, what are its slope and y-intercept?
    The slope is 1 and the y-intercept is -3.
  • Given the equation y = 2/3x - 1, what point does the line cross the y-axis?
    It crosses the y-axis at (0, -1), since the y-intercept is -1.