Mr. Kone Math Hub · Review sheet

Slope and Rate of Change

Unit 3: Slope, Rate of Change & Linear Equations · NY-8.EE.5, NY-8.EE.6, AI-F.IF.6

Both exams

Notes

Rise over run is a rate. If a subway line rises 12 meters over 3 seconds, the slope is 4 meters per second. The sign of slope tells direction: positive means both variables increase together; negative means one increases while the other decreases.

Same slope everywhere. On a non-vertical line, similar slope triangles show that every pair of points gives the same m. That is why one pair of points is enough to find the slope of a line.

Algebra I extension. For a nonlinear function, we still compute (f(b) − f(a))/(b − a). That average rate of change is the slope of the secant, not the whole graph.

Vocabulary

  • slope: The ratio of vertical change to horizontal change between two points on a line.
  • unit rate: A rate with a denominator of 1.
  • rate of change: How one quantity changes with respect to another.

Practice (no calculator unless marked)

  1. What is the y-intercept of the line that passes through the points (−1, 5) and (2, −1)?
    • A. −1
    • B. −2
    • C. 3
    • D. 5
  2. What is the y-intercept of the line that passes through the points (−1, 5) and (2, −1)?
    • A. −1
    • B. −2
    • C. 3
    • D. 5
  3. What is the y-intercept of the line that passes through the points (−1, 5) and (2, −1)?
    • A. −1
    • B. −2
    • C. 3
    • D. 5
  4. What is the y-intercept of the line that passes through the points (−1, 5) and (2, −1)?
    • A. −1
    • B. −2
    • C. 3
    • D. 5
  5. What is the y-intercept of the line that passes through the points (−1, 5) and (2, −1)?
    • A. −1
    • B. −2
    • C. 3
    • D. 5
  6. What is the y-intercept of the line that passes through the points (−1, 5) and (2, −1)?
    • A. −1
    • B. −2
    • C. 3
    • D. 5
  7. What is the y-intercept of the line that passes through the points (−1, 5) and (2, −1)?
    • A. −1
    • B. −2
    • C. 3
    • D. 5
  8. What is the y-intercept of the line that passes through the points (−1, 5) and (2, −1)?
    • A. −1
    • B. −2
    • C. 3
    • D. 5