From Table to Graph: Plotting y = 2x + 1
Fill the table, plot the points, and draw the line. Watch how the equation becomes a picture.
Equation
y = 0.5x − 1
Graph
Table
| x | y |
|---|---|
| -2 | -2 |
| -1 | -1.5 |
| 0 | -1 |
| 1 | -0.5 |
| 2 | 0 |
What this lesson covers
What you do
You shape the function y = m*x + c and watch the graph answer.
Challenges to clear
- Build y = 2x + 1: the line passes through (0, 1).
- And through (1, 3) — fill the table, then the picture draws itself.
- Your turn with a steeper line: y = 4x − 3. Read the x = 0 row of the table first — it must show −3, so set the intercept there.
- Now the x = 2 row must read 5. Slide the slope until it does — the table fills in and the graph draws itself.
Check yourself
Why do we need at least two points to draw a straight line?
In the equation y = 2x + 1, what does the '1' represent on the graph?
- Two points uniquely determine a straight line; one point could belong to infinitely many lines. — correct
- Because we need to check if the line is vertical or horizontal.
- Because the first point might be calculated wrong.
- Because the graph paper has grid lines every two units.
- The y-intercept: where the line crosses the vertical axis. — correct
- The slope: how steep the line is.
- The x-intercept: where the line crosses the horizontal axis.
- The starting value of x.
Think about it
- If we change the '2' in 2x to a '1', will the line get steeper or flatter?