The Coordinate Plane and Slope
Flashcards covering slope formula, special cases, tables, graphs, and rate interpretation.
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Questions Covered in This Set
10 cards to master
Slope formula for points (x₁, y₁) and (x₂, y₂)
m = (y₂ − y₁) / (x₂ − x₁) = rise/run — the change in y for each 1 unit increase in x.
What does a point (x, y) tell you to do?
Run first, then rise: x is horizontal movement, y is vertical. So (3, −2) = 3 right, 2 down.
Slope of a horizontal line (y = c)
m = 0 — there is no rise.
Slope of a vertical line (x = c)
Undefined — the run is 0 and you can't divide by zero. Memory hook: VUX (Vertical, Undefined, x =).
Find the slope through (2, 3) and (6, 11)
m = (11 − 3)/(6 − 2) = 8/4 = 2. Reversing both points gives (3−11)/(2−6) = 2, the same answer.
How do you tell if a table is linear?
The change in y must be constant for each constant change in x. If the ratio Δy/Δx isn't the same for all pairs, it isn't linear.
Table: x = 1, 3, 5, 7 and y = 10, 4, −2, −8. Slope?
x increases by 2, y drops by 6, so m = −6/2 = −3. Check outer points: (−8−10)/(7−1) = −3. ✓
Biggest trap when reading slope off a graph
Assuming each gridline equals 1. Always read the scale — boxes may be worth 2, 5, or 10, which changes the rise and run.
In C = 45 + 12h (tutor cost in dollars for h hours), what does 12 mean?
The cost increases by $12 for each additional hour — slope is a rate with units (y-units per x-unit).
Points (4, k) and (6, 13) lie on a line of slope 5. Find k.
(13 − k)/(6 − 4) = 5 → 13 − k = 10 → k = 3.
