On the Line or Not?
Part of the Graphs & Systems section of Coddy's Algebra journey. Lesson 8 of 64.
Whether a point lies on a line is a question the rule answers without any drawing: substitute and compare. Is (4, 5) on y = 2x - 3? The rule at x = 4 gives
y = 2(4) - 3 = 5
and 5 is exactly the y of the point, so yes. Is (3, 4) on it? The rule gives 2(3) - 3 = 3, not 4, so no: the point floats one step above the line.
This is the meaning of "solution" for a two-variable equation: a pair (x, y) that makes it true. A line is nothing but the picture of all its solutions at once.
Challenge
The point (3, k) lies on the line y = 3x - 2. Find k.
Try it yourself
Solve for k
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