Question 1 of 3Both examsAI-F.IF.6Algebra I Regents · June 2024 · Q10Non-calculatorproficient
What is the y-intercept of the line that passes through the points (−1, 5) and (2, −1)?
Choose or type an answer first. The key stays hidden until you do.
Unit 3 · Slope, Rate of Change & Linear Equations
Slope and Rate of Change
Slope m = (y₂ − y₁)/(x₂ − x₁) is the constant rate of change of a linear function and the unit rate of a proportional graph.
NY-8.EE.5NY-8.EE.6AI-F.IF.6
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.
Example: Through (1, 2) and (4, 8), m = 6/3 = 2.
unit rate
A rate with a denominator of 1.
Example: 60 miles in 2 hours is a unit rate of 30 miles per hour.
rate of change
How one quantity changes with respect to another.
Example: A savings account that grows $15 each week has a rate of change of 15 dollars per week.
Worked examples
Try the prompt first. The steps stay folded until you ask to see them.
Two points
Find the slope of the line through (−2, 5) and (4, −1).
Common errors
Watch for
Writing run/rise or subtracting in inconsistent order
The order of y's must match the order of x's.
Fix: Label the points as 1 and 2 and keep that order.
Watch for
Calling a vertical line slope 0
Horizontal lines have slope 0; vertical lines have undefined slope.
Fix: Zero in the denominator means undefined.
Instructional videos
External links. We do not host copyrighted exam items or paid video libraries.
- Khan Academy: Slope — Khan Academy (external)
Explore with an applet
Guided practice
Submit each answer to check it. The key is not shown until you do.
Question 2 of 3Both examsAI-F.IF.6Algebra I Regents · June 2024 · Q10Non-calculatorproficient
What is the y-intercept of the line that passes through the points (−1, 5) and (2, −1)?
Choose or type an answer first. The key stays hidden until you do.
Question 3 of 3Both examsAI-F.IF.6Algebra I Regents · June 2024 · Q10Non-calculatorproficient
What is the y-intercept of the line that passes through the points (−1, 5) and (2, −1)?
Choose or type an answer first. The key stays hidden until you do.
Intervention
Use a digital graph applet and count grid squares for rise and run.
Enrichment
Show that three points are collinear by comparing pairwise slopes.
Explain your reasoning
Sentence starters · Notice and Wonder · Three Reads · Think-Pair-Share · Compare and Connect · Math Talk · Stronger and Clearer Each Time
- The slope is …, which means for every 1 unit of x, y …
- I subtracted in the same order because…