Plotting y = 2x + 1
Calculate three points, check the pattern, and draw the line.
Equation
y = x
Graph
Table
| x | y |
|---|---|
| -1 | -1 |
| 0 | 0 |
| 1 | 1 |
| 2 | 2 |
| 3 | 3 |
What this lesson covers
What you do
You shape the function y = m*x + c and watch the graph answer.
Challenges to clear
- Build the line y = 2x + 1: it must pass through (1, 3).
- And through (2, 5) — two points pin the line down exactly.
- Build y = 3x − 2 yourself. Start with where it cuts the y-axis: (0, −2).
- Now find the slope: the line must also pass (2, 4). Rise 6 over run 2 — that is m = 3.
Check yourself
Why do we plot at least three points for a linear equation?
- To check if they form a straight line, which confirms our calculations are correct. — correct
- Because the first two points might be too close to see clearly.
- Because linear equations always require three points to define a slope.
- To make the graph look fuller and more complete.
Think about it
- For y = 2x + 1: what is y when x is 0? And when x is 1?