Skill: line-forms

Line Forms Practice

An endless supply of never-repeating conversion problems: write point-slope from a point and slope, convert between all three forms, and read intercepts straight from standard form.

1 Practice

Type your answer and press Check answer (or Enter). A wrong answer earns a hint first; a second miss walks you through the full solution.

Score 0 · Streak 0 · Problem 0

Score counts first-try correct answers. Streak counts consecutive correct answers.

Problem

How to enter answers

Point-slope: type y-2=3(x-1) — spaces are fine, e.g. y - 2 = 3(x - 1).
Standard: type 2x-y=5 or 2x - y = 5, integers with A positive.
Slope-intercept: type y=2x+3 as usual.
Intercepts: plain numbers or fractions.

2 What you’ll practice

Every problem is generated fresh from templates across several question types — a problem never repeats until its whole pool is used up.

Point-slope

The right tool for point-plus-slope — with the sign trap built in.

(1, 2), m = 3 → y−2 = 3(x−1)

Convert

All three forms, every direction. Distribute, clear, rearrange.

y = 2x−5 → 2x−y = 5

Intercepts

Standard form gives both intercepts with zero graphing.

2x−4y = 8 → x-int 4, y-int −2

3 Watch out for these

The mistakes students make most often on these problems.

1. Sign errors in point-slope

Wrong: (−2, −5), m = 2 → y − 5 = 2(x − 2). Right: y + 5 = 2(x + 2).

2. Using y = mx + b for point-plus-slope

Wrong: always solving for b first. Right: point-slope is built for this.

3. Negative A in standard form

Wrong: −2x + 3y = 6. Right: 2x − 3y = −6.

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