CCSS.MATH.8.F.B.4✓ New York State Education Department (NYSED) AlignedAcademic Year 2026–27
Slope, Rate of Change & Linear Graphing (y = mx + b)
Calculate constant rate of change (slope = rise / run) from tables, graphs, and two coordinate points; graph lines using slope-intercept form.
Why It Matters:Underpins speed calculations (miles per hour), fuel efficiency, monthly utility bills, and financial depreciation curves.
Curated Video Instruction
● Verified Active EmbedSTEP-BY-STEP PROOF
Worked Example
Find the slope of the line passing through points (2, 3) and (6, 11):
1
Apply Slope Formula
m = (y2 - y1) / (x2 - x1)
Calculates vertical change (rise) over horizontal change (run).
2
Substitute coordinates
m = (11 - 3) / (6 - 2) = 8 / 4
Subtract corresponding y-values and x-values.
3
Simplify ratio
m = 2
The slope is 2 (for every 1 unit right, the line ascends 2 units).
✓Verification Check
Confirm using point-slope form: y - 3 = 2(x - 2) -> y = 2x - 1. Plug in x=6: 2(6)-1 = 11.
y = 2(6) - 1 = 11
•
11 = 11 (Verified)
⚠️ Common Pitfalls & Misconceptions
Putting run over rise instead of rise over run
✗ Computing slope as (x2 - x1) / (y2 - y1)✓ Slope is vertical change divided by horizontal change: delta y / delta x
Rise (vertical / y) is always in the numerator; run (horizontal / x) is in denominator.
INTERACTIVE DRILLS
Guided Practice
Practice Question1 of 1
Step-by-step Feedback
In the linear equation y = -3x + 5, what is the slope of the line?
MASTERY BENCHMARK
Official Assessment Quiz
Formal Assessment
Slope, Rate of Change & Linear Graphing (y = mx + b)
Passing Criteria:70% or higher
Question 1 of 1
What is the slope of a horizontal line?
Education to Career Navigation
Where This Lesson Leads
Civil Engineers design road grades; Financial Traders model stock momentum slopes.