Algebra
Graphing Linear Equations – Table, Plot, Draw
Graphing a linear equation like y = mx + c follows a reliable three-step procedure: build a table of values (choose a few x-values and calculate the matching y-values), plot each pair as a point on the coordinate plane, and then draw a straight line through them. Since a straight line is fully determined by just two points, technically only two table rows are needed – but a third is a good habit, as a useful check that your calculations are correct.
This procedure works for any linear equation, no matter its gradient or intercept, and it's the same practical skill you'll rely on throughout the rest of this course whenever a problem calls for an accurate hand-drawn graph.
The Table-Plot-Draw Procedure
Choose a few x-values, calculate y using the equation, plot each (x, y) point, then draw a straight line through them.
y = 2(4) − 3 = 8 − 3 = 5. Plot the point (4, 5).
Real-Life Application
- Engineering drawings: plotting precise straight-line paths from a table of coordinates.
- Data visualisation: graphing a trend line from a small set of calculated points.
- Navigation charts: plotting a straight course between calculated waypoints.
Key Takeaways
- Graphing a linear equation follows the steps: table, plot, draw.
- Only two points are strictly needed, since two points define a straight line.
- A third point is a useful accuracy check.