On the Line or Not?
Part of the Graphs & Systems section of Coddy's Algebra journey. Lesson 8 of 64.
You can tell whether a point lies on a line without drawing anything. Substitute the x-coordinate of the point into the rule and compare the result with the y-coordinate. Is (4, 5) on the line y = 2x - 3? At x = 4 the rule gives
y = 2(4) - 3 = 5
The result 5 matches the y-coordinate of the point, so (4, 5) is on the line. Is (3, 4) on the line? At x = 3 the rule gives 2(3) - 3 = 3, not 4. So (3, 4) is not on the line. It is one unit above it.
A solution of an equation in x and y is an ordered pair that makes the equation true. For this linear equation, the graph is the line containing all those solution points.
Challenge
EasyThe point (3, k) lies on the line y = 3x - 2. Find k, the value of y on the line at x = 3.
Try it yourself
Solve for y
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