Ax + By = C

Part of the Graphs & Systems section of Coddy's Algebra journey. Lesson 25 of 61.

A linear equation can also be written in standard form, $Ax+By = C$ , where A and B are not both zero. For example, $2x+3y = 12$ . Setting one coordinate to zero lets you find an intercept, if it exists.

On the x-axis, $y = 0$ . Substituting into $2x+3y = 12$ gives $2x = 12$ , so the x-intercept is $\left(6, 0\right)$ .

Challenge

Medium

The line $3x+4y = 24$ crosses the x-axis where y = 0. Find the x value of that crossing.

Try it yourself

3x+4y = 24

y = 0

Get $x$ alone

All lessons in Graphs & Systems

1Points and Rules

Two Numbers, One Point A Rule Makes Points The Points Line Up

4Slope-Intercept Form

y = mx + b The Starting Height Write the Equation Solve for y Draw From Any Form Recap: y = mx + b

7Parallel & Perpendicular

Same Slope, Never Meet The Perpendicular Slope A Right-Angle Line Recap: Two Relations

10Systems by Graphing

Two Lines, One Answer Solve by Drawing Check the Crossing When Lines Never Cross Recap: By Graphing

2The Whole Plane

The Four Quadrants Mirror Points On the Line or Not?Recap: Rule to Line

5Point-Slope Form

A Point and a Slope From Two Points Flat or Vertical Through Draw From a Point Recap: Point-Slope

8Function Notation

The Name of a Rule Inputs With Signs Find the Input The Graph of f Recap: f(x)

11Solving Systems Exactly

Substitution Isolate First Elimination Scale, Then Add Three Unknowns Two Numbers, Two Facts Recap: Two Methods