Functions — Introduction
GradesAlgebra IFunctions — IntroductionLinear Functions & Their Graphs

Linear Functions & Their Graphs

📈 Functions — Introduction
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Linear Functions & Their Graphs

Graph lines and interpret slope as a rate of change.

A linear function has the form f(x) = mx + b, where m is the slope (rate of change) and b is the y-intercept. Slope measures how steeply the line rises or falls per unit increase in x.

m=ΔyΔx=y2−y1x2−x1m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}

Forms of a Linear Equation

Slope-intercept: y = mx + bPoint-slope: y − y₁ = m(x − x₁)Standard: Ax + By = C

Each form is useful in different situations — choose the one that matches the given information.

Average Rate of Change=f(b)−f(a)b−a\text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a}
🏔️Finding the Equation of a Line
Find the equation through (2, −1) with slope 3. Using point-slope form: y − (−1) = 3(x − 2) → y + 1 = 3x − 6 → y = 3x − 7.
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Remember This!

Parallel lines have equal slopes. Perpendicular lines have slopes that are negative reciprocals: if one slope is m, the perpendicular slope is −1/m.

✏️ Try It!

What is the slope of the line passing through (−1, 4) and (3, −8)?

Practice with CalcVerse
📈Line Grapher (y = mx + b)
Take Quiz 📝 — 24 Questions