Draw by Intercepts
Part of the Graphs & Systems section of Coddy's Algebra journey. Lesson 30 of 64.
The two intercepts are two points on the line, and two points are enough to draw it. For x + 2y = 4, setting y = 0 gives the x-intercept (4, 0), and setting x = 0 gives the y-intercept (0, 2). Draw the line through those two points. For an equation in standard form, this is usually the fastest way to draw the graph, because you do not need to rearrange the equation.
The method does not work in two cases. If the line passes through the origin, both intercepts are the same point, (0, 0). The equation is then y = mx for some slope m, and you need a second point from another substitution, such as x = 1. If one variable is missing from the equation, the line is flat or vertical and crosses only one axis.
Challenge
MediumDraw 4x + 3y = 12 using its two intercepts.
Try it yourself
Draw the graph
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