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Precalculus: Lines and Slopes

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  • What is the formula to find the slope of a line given two points?
    The slope \(m\) is \(\frac{y_2 - y_1}{x_2 - x_1}\), where (x1, y1) and (x2, y2) are the two points.
  • What does a positive slope indicate about a line?
    A positive slope means the line rises from left to right.
  • What does a negative slope indicate about a line?
    A negative slope means the line falls from left to right.
  • What is the slope of a horizontal line?
    The slope of a horizontal line is \(0\).
  • What is the slope of a vertical line?
    The slope of a vertical line is undefined.
  • What is the point-slope form of a line's equation?
    Point-slope form is \(y - y_1 = m(x - x_1)\), where m is slope and (x1, y1) is a point on the line.
  • What is the slope-intercept form of a line's equation?
    Slope-intercept form is \(y = mx + b\), where m is slope and b is the y-intercept.
  • What is the equation of a horizontal line?
    A horizontal line has the form \(y = b\), where b is the y-intercept.
  • What is the equation of a vertical line?
    A vertical line has the form \(x = a\), where a is the x-intercept.
  • What is the general form of a line's equation?
    General form is \(Ax + By + C = 0\), where A, B, and C are integers and A ≥ 0.
  • How do you graph a line using slope and y-intercept?
    1. Plot the y-intercept (0, b). 2. Use slope m as rise over run to find a second point. 3. Draw a line through the points with arrows at ends.
  • How do you find the x-intercept of a line in general form?
    Set y = 0 and solve for x to find the x-intercept.
  • How do you find the y-intercept of a line in general form?
    Set x = 0 and solve for y to find the y-intercept.
  • How do you graph a line using intercepts?
    1. Find x-intercept by setting y=0. 2. Find y-intercept by setting x=0. 3. Draw a line through these intercept points with arrows at ends.
  • What is the slope of the line passing through points (4, -1) and (3, -1)?
    The slope is 0, so the line is horizontal with equation \(y = -1\).
  • What is the slope of the line passing through points (3, -4) and (3, 5)?
    The slope is undefined, so the line is vertical with equation \(x = 3\).
  • What does the slope-intercept form tell you about a line?
    It shows the slope m and the y-intercept b directly in the equation \(y = mx + b\).
  • How can you write the equation of a line given slope and a point?
    Use point-slope form: \(y - y_1 = m(x - x_1)\).
  • What is the significance of the coefficients A, B, and C in the general form?
    They define the line equation \(Ax + By + C = 0\), where A and B are not both zero.
  • What is the method to graph a line from its general form equation?
    Find x- and y-intercepts by setting y=0 and x=0 respectively, then draw the line through these points.