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PEAZIT Aha card

Slope tells how y changes for a step in x

Slope m is change in y divided by change in x. The number b is the y-intercept, where x = 0.

The line through (1; 3) and (3; 7) has equation y = 2x + 1.

Relation	Meaning
y = mx + b	Choose this form for a nonvertical line.
m = (7 − 3)/(3 − 1) = 2	When x increases by 2, y increases by 4.
3 = 2 × 1 + b; b = 1	Substitute a known point to find b.

One worked example

y = mx + bChoose this form for a nonvertical line.
m = (7 − 3)/(3 − 1) = 2When x increases by 2, y increases by 4.
3 = 2 × 1 + b; b = 1Substitute a known point to find b.

Watch out: A vertical line has form x = constant and no finite slope. The change in x cannot be zero when calculating m.

Goal, prerequisites and card origin

What you will learn: Use the line equation y = mx + b.

What you need first: Coordinates and linear equations.

An original PEAZIT working card. Independent expert review and effectiveness testing have not yet taken place. · v1

Show connections

A system: both conditions at once

x + y = 5 — its line passes through the — Intersection of the lines

x − y = 1 — its line also passes through the — Intersection of the lines

Intersection of the lines — has coordinates — Ordered pair (3, 2)

Ordered pair (3, 2) — satisfies: 3 + 2 = 5 — x + y = 5

Ordered pair (3, 2) — satisfies: 3 − 2 = 1 — x − y = 1

Slope m is change in y divided by change in x. The number b is the y-intercept, where x = 0.

Without JavaScript, write your answer elsewhere before opening the solution.On line y = 3x − 1, take x = 4. What is y? Enter a number.

Solution — open after your own attempt

11 3 × 4 − 1 = 11.

A question for your next return: A line passes through (0; 5) and (2; 1). What is its slope? Enter a number.

Solution — open after your own attempt

-2 (1 − 5)/(2 − 0) = −4/2 = −2.

Catalogue

Book

WikibooksEN

Basic Algebra/Lines (Linear Functions)/Slope-Intercept Form of a Line

Link to the page “Basic Algebra/Lines (Linear Functions)/Slope-Intercept Form of a Line” in Wikibooks. Subject assignment uses its title and source categories.