Slope: measurement of a straight line’s steepness or incline, represented by m
Positive Slope: measurement when a line’s right end is higher than its left end
Negative Slope: measurement when a line’s left end is higher that its right end
Zero Slope: measurement of a horizontal line, when there is no change in y-points

RULES FOR SLOPE PROBLEMS
1) Slope Formula: y = mx + b
     y represents the y-coordinate; x represents the x-coordinate
     m represents the slope of the line; b is a constant (a number)
2) Slope Calculation: (y₂ - y₁) / (x₂ - x₁)
3) Horizontal lines have a slope of zero because change in y is equal to zero (m = 0)
4) Vertical lines have an undefined slope because change in x is equal to zero
5) A rising 45° line has a slope equal to 1; a falling 45° line has a slope equal to -1
6) Parallel lines have slopes that are equal (ex. m₁ = 1 /2, m₂ = 1/2)
7) Perpendicular lines have slopes that are negative reciprocals (ex. m₁ = 1/2, m₂ = -2)

SAMPLE PRACTICE QUESTIONS FOR SLOPES

1. If (2, 4) is a point on the line, what is the slope of function y + 2 = mx?

      Solution
      A) Put function into form of slope formula
           y + 2 = mx --> y = mx - 2

      B) Solve for m
           y = mx - 2 --> 4 = (m)(2) - 2 --> 2m = 6 --> m = 3

2. Line l passes through the points (1, 3) and (-2, -4). What is the reciprocal of the slope of l?

     Solution
    A) Solve for Slope
        (y₂ - y₁) / (x₂ - x₁) --> (3 - -4) / (1 - - 2) --> 7/3

     B) Don't forget it's the reciprocal
          Reciprocal of 7/3 = 3/7

SAT Math: Slope Problems

Lesson Includes:

—Math Terms for Slope Problems

—Tips for Slope Problems

—Sample Practice Questions

—Practice Questions

Math

SAT Reading

SAT Writing

SAT Vocabulary

SLOPE REVIEW QUIZ

 

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