Three Forms of a Line
Practice slope-intercept, point-slope, and standard form plus the conversions between them.
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Questions Covered in This Set
10 cards to master
Slope-intercept form
y = mx + b, where m is the slope and b is the y-intercept (value of y when x = 0).
Point-slope form
y − y₁ = m(x − x₁) — use it when you know a slope and one point on the line.
Standard form
Ax + By = C, with x and y on the same side and usually integer coefficients.
Slope shortcut for Ax + By = C
m = −A/B. Example: 3x + 5y = 30 has slope −3/5.
How do you find the intercepts of Ax + By = C fast?
Plug in zeros: x = 0 gives y = C/B; y = 0 gives x = C/A. For 3x + 5y = 30: (0, 6) and (10, 0).
In y = 12 + 0.5x, what is the slope?
0.5 — the slope is always the coefficient attached to x, not the first number you see.
Line with slope 4 through (2, −3): write and simplify
y + 3 = 4(x − 2) → y + 3 = 4x − 8 → y = 4x − 11.
Given two points, how do you write the equation?
Find m = (y₂ − y₁)/(x₂ − x₁), then plug m and either point into point-slope form; check with the other point.
Convert y = (2/3)x − 4 to standard form
Multiply by 3: 3y = 2x − 12, so 2x − 3y = 12.
Find the slope and y-intercept of 6x − 2y = 14
−2y = −6x + 14 → y = 3x − 7; slope 3, y-intercept (0, −7).
