Algebra 1A — Equations & Lines

Lines: slope, intercept & graphing

continues from lesson 2 — values defined earlier in the course stay live here

ELI5: a straight line is a steady rate. The slope says how much y climbs for each step right in x (rise ÷ run); the intercept says where the line crosses x = 0. Any two points lock in the whole line.

xa = 1

ya = 3

xb = 5

yb = 11

slope = \frac{yb - ya}{xb - xa}

2

rise over run = 2

y_{int} = ya - slope \cdot xa

1

back up to x = 0: intercept 1

slope * x + y_int

the line through both points — move a point and watch it tilt

Real-world hook: slope is the everyday "per": miles per hour on a distance–time graph, dollars per unit on a cost graph, degrees per minute as a pan heats up.

Try it yourself: find the slope of the line through (2, 1) and (5, 10).

slope_{you} = 3

✏️ Your turn: find the slope through (2, 1) and (5, 10). The check sees whether a line of your slope, starting at (2, 1), actually reaches (5, 10).

✓ pass

\mathrm{abs}\left(slope_{you} \cdot \left(5 - 2\right) + 1 - 10\right) < 10^{-9}

green when your line hits (5, 10)

Where next: Algebra 1B uses these moves on two unknowns at once, tames exponents, and learns to factor.