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Linear Functions

Build confidence with slope, equations, graphs, and real-world linear models.

What you will practice

  • Find slope from graphs, tables, equations, and points
  • Write equations of lines
  • Interpret rate of change
  • Compare linear models
  • Identify parallel and perpendicular lines

Why it matters

Linear functions show up across Math 1: tables, graphs, word problems, scatter plot models, and comparison questions. A steady slope strategy makes the rest of the course feel more connected.

Words and forms to know

These terms support equation writing, graph interpretation, and EOC-style modeling questions.

Slope

The steepness of a line, found by comparing vertical change to horizontal change.

Rate of Change

How much the output changes for each 1-unit change in the input.

Y-Intercept

The output value when the input is 0; where a graph crosses the y-axis.

X-Intercept

The input value when the output is 0; where a graph crosses the x-axis.

Slope-Intercept Form

A line written as y = mx + b, where m is slope and b is the y-intercept.

Standard Form

A linear equation written as Ax + By = C.

Point-Slope Form

A line written using one point and the slope: y - y1 = m(x - x1).

Parallel Lines

Lines in the same plane that never intersect and have the same slope.

Perpendicular Lines

Lines that meet at a right angle and have slopes that are opposite reciprocals.

Linear Model

An equation, graph, or table that represents a constant rate of change.

Choose a Linear Functions set

Start with DOK 1 fluency, then build toward analysis and EOC-style mixed practice.