Unit 9: Equations of Linear Relations (Math 10C)
Slope-intercept, writing linear equations, general form, point-slope, graphing, and rate of change.
Slope-Intercept \(y=mx+b\)
Point-Slope \(y-y_1=m(x-x_1)\)
General \(Ax+By+C=0\)
Rate of Change \(\Delta y/\Delta x\)
Graphing & Intercepts
What You Should Be Able To Do
- Write equations of lines from slope & intercept, one point & slope, two points, or general form.
- Convert between slope-intercept, point-slope, and general forms; identify intercepts.
- Graph linear relations accurately and interpret slope as rate of change.
- Determine rate of change from tables, graphs, or context and connect to \(m\).
Progress autosaves to this device.
Video Library
Interactive Tools
Equation Writer / Converter + Grapher
Table → Line & Rate of Change
Context Builder (Rate & Initial Value → Equation)
Build \(y=mx+b\) from Words
Quick Reminders
- Slope \(m=\dfrac{\Delta y}{\Delta x}=\dfrac{y_2-y_1}{x_2-x_1}\).
- From two points: find \(m\), then \(b=y_1-mx_1\).
- General \(\to\) slope-intercept: if \(B\neq0\), \(y=-\dfrac{A}{B}x-\dfrac{C}{B}\).
- Vertical line: \(x=k\) (no slope, no \(y\)-intercept).
- Horizontal line: \(y=k\) (\(m=0\)).
Unit 9 Quizzes
Downloadable Review
Quick Practice Scratchpad
Try: Line through \((-3,5)\) with slope \(-\tfrac{2}{3}\). Convert \(3x-2y+6=0\) to \(y=mx+b\). From points \((1,4)\) and \((5,12)\), write the equation.