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Lines quiz

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  • What is the mathematical definition of slope for a line between two points?
    Slope is defined as (y2 - y1) / (x2 - x1), representing the ratio of vertical change to horizontal change between two points.
  • What does a positive slope indicate about the direction of a line?
    A positive slope means the line rises from left to right.
  • What is the slope of a horizontal line and how is its equation typically written?
    The slope of a horizontal line is 0, and its equation is written as y = b, where b is a constant.
  • What is the slope of a vertical line and how is its equation typically written?
    The slope of a vertical line is undefined, and its equation is written as x = a, where a is a constant.
  • What is the slope-intercept form of a line and what do the 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 its slope-intercept form?
    First plot the y-intercept, then use the slope (rise over run) to find another point, and connect the points with a straight line.
  • What is the point-slope form of a line and when is it used?
    The point-slope form is y - y1 = m(x - x1), used when you know the slope and a point (x1, y1) on the line.
  • How do you convert point-slope form to slope-intercept form?
    Expand and solve for y to isolate it, resulting in y = mx + b.
  • How do you find the slope if you are given two points on a line?
    Use the formula (y2 - y1) / (x2 - x1) to calculate the slope.
  • What is the standard form of a line equation and how can you find the slope and y-intercept from it?
    The standard form is Ax + By + C = 0; solve for y to convert it to slope-intercept form and identify the slope and y-intercept.
  • How do you find the x-intercept from a line in standard form?
    Set y = 0 in the equation and solve for x.
  • How do you find the y-intercept from a line in standard form?
    Set x = 0 in the equation and solve for y.
  • What is the relationship between the slopes of parallel lines?
    Parallel lines have identical slopes 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.
  • How do you write the equation of a line parallel or perpendicular to a given line?
    Use the same slope for parallel lines or the negative reciprocal for perpendicular lines, and apply either slope-intercept or point-slope form depending on the information given.