Lesson 4 — Point-Slope & Standard Forms

Use y − y₁ = m(x − x₁) and Ax + By = C to describe lines, convert between forms, and find intercepts.

Given slope m (e.g., velocity in m/s) and a point (x₁,y₁) (e.g., position at time t₁): y − y₁ = m(x − x₁).

Example: For m = 2, (x₁,y₁) = (1,3), the equation is y − 3 = 2(x − 1), meaning a velocity of 2 m/s through position (1,3).

Ax + By = C (often integers, A ≥ 0). Find intercepts: set one variable to 0.

Example: 3x + 2y = 12 → x-intercept: (4,0) (set y=0); y-intercept: (0,6) (set x=0).

Sandbox — Form Converter

Point-Slope inputs

(x₁, y₁) ( , )

Standard form inputs

Point-Slope (input)

y − 2 = −½(x + 3)

Slope-Intercept

y = −½x + ½

Standard

x + 2y = 1

Enter values and click a convert button.

Question 1 of 5

For 3x + 2y = 12, the x-intercept is (4,0).

More practice (unlocks as you answer correctly)