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)
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
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
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
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
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
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
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
What is the y-intercept of the line that passes through the points (−1, 5) and (2, −1)?