Ax + By = C
Part of the Graphs & Systems section of Coddy's Algebra journey. Lesson 28 of 64.
Lines also travel as 2x + 3y = 12: both variables on one side, a number on the other. This is standard form, Ax + By = C, and it hides the slope but hands over something else cheaply: the crossings with the axes.
On the x-axis, y is 0; substituting y = 0 into 2x + 3y = 12 leaves 2x = 12, so the line crosses at (6, 0). The x-intercept costs one substitution, no rearranging at all.
Challenge
The line 3x + 4y = 24 crosses the x-axis where y = 0. Find the x value of that crossing.
Try it yourself
Solve for x
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Graphs & Systems
1The Coordinate Plane
Two Numbers, One PointThe Four QuadrantsPoints on the AxesMirror PointsRecap: The Plane4Slope-Intercept Form
y = mx + bThe Starting HeightWrite the EquationSolve for yDraw From Any FormRecap: y = mx + b7Parallel & Perpendicular
Same Slope, Never MeetThe Perpendicular SlopeA Right-Angle LineRecap: Two Relations2From Rule to Line
A Rule Makes PointsThe Points Line UpOn the Line or Not?Between the DotsRecap: Rule to Line