In this lesson you’ll learn the coordinate plane, how to plot points, and how to graph basic lines using tables or slope-intercept form.
The coordinate plane is a grid with a horizontal x-axis and vertical y-axis intersecting at the origin (0,0).
Points are written as (x,y). x tells horizontal position, y vertical.
Quadrants:
- I: (+x,+y) - upper right
- II: (−x,+y) - upper left
- III: (−x,−y) - lower left
- IV: (+x,−y) - lower right
To plot (3,−2): go right 3, down 2.
The four quadrants and a plotted point
Graphing lines: Make a table of x and y values from the equation, plot points, connect with a straight line.
Example: y=2x+1
| x | y |
|---|
| 0 | 1 |
| 1 | 3 |
| 2 | 5 |
| −1 | −1 |
Plot points (0,1), (1,3), (2,5), (−1,−1) → draw line.
y = 2x + 1
Slope-intercept form: y=mx+b
- m = slope (rise/run)
- b = y-intercept (where line crosses y-axis)
Graph y=−3x+4
- y-intercept b=4 → point (0,4)
- Slope m=−3=1−3 → down 3, right 1
- From (0,4): right 1 → x=1, down 3 → y=1 → point (1,1)
- Plot (0,4) and (1,1), draw straight line.
| x | y |
|---|
| 0 | 4 |
| 1 | 1 |
| 2 | −2 |
y = -3x + 4
Graphing helps visualize relationships:
- Budget line: y=income−0.30x (spending)
- Distance over time: y=speed×x (hours)
- Cost vs quantity: y=fixed cost+variable cost×x
- Temperature conversion: F=59C+32 (linear graph)
These show trends, break-even points, or comparisons in money, work, or science.
