Co-ordinate Geometry
285. Plotting the Line · Connecting points to reveal the graph
Point P always lies on the line y = mx + c.
To graph a linear equation y = mx + c, find a few points that satisfy it, plot them, and join them with a ruler. Because the equation is linear, the points always lie on one straight line.
What this lesson covers
Try to break it
Drag P along the line. At every position the coordinates satisfy y = 2x + 1 — try to find a P on the line where they don't. Now imagine pulling P to (5, 3): that point sits off the line because 2(5) + 1 = 11 ≠ 3. Only points whose coordinates satisfy the equation belong on the graph.
How you build it
Plot points of y = 2x + 1 and join them into a line.
- Point tool: plot A at (-1, -1) — a point that satisfies y = 2x + 1.
- Point tool: plot B at (0, 1) — the y-intercept.
- Point tool: plot C at (1, 3).
- Line tool: click A, then C — the straight line passes through all three points. They are collinear because y = 2x + 1 is linear.
The proof, step by step
Prove that point P lies on the line y = mx + c.
- The graph of a linear equation is a straight line.
- Any point on the line satisfies the equation.
- The equation is satisfied by the coordinates of any point on the line.
Worked example
Draw the graph of the equation y = 3x - 2. From the graph, find the value of y when x = 2.
Substitute x = 2 into the equation: y = 3(2) - 2 = 6 - 2 = 4.
- 4 — correct
- 6
- 8
- 2