When a linear function is written in slope intercept form, two pieces of information — the slope and y-intercept of a line — are obvious.
Slope Intercept Form
y = mx + b, where m is the slope and b is the y-intercept.
In other words, the slope is the coefficient of x (or the number before x) and the y-intercept is the constant. Equipped with a slope and y-intercept, you can graph any line.
The following examples detail how to graph a line. Use graph paper.
1. Graph of y = 10 - x
1. Rewrite the -x as + - 1x:
y = 10 + -1x
Now, it's easier to identify the slope.
2. Identify the y-intercept and slope:
- y-intercept: (0,10)
- slope: -1 or -1/1
3. Plot the point (0,10).
4. Put your finger on (0,10). Slope is -1/1. Think rise/run. Move down 1 unit and to the right 1 unit. Place a dot here. You should be at the point (1,9)
5. Draw a straight line between (0,10) and (1,9) that stretches across the entire Cartesian Plane.
6. Compare your graph to my graph.
2. Graph of y = 16 + 5x
1. Identify the y-intercept and the slope:
- y-intercept: (0,16)
- slope: 5 or 5/1
2. Plot the point (0,16).
3. Put your finger on (0,16). Slope is 5/1. Think rise/run. Move up 5 units and to the right 1 unit. Place a dot here. You should be at the point (1,21).
5. Draw a straight line between (0,16) and (1,21) that stretches across the entire Cartesian Plane.
6. Compare your graph to my graph.
3. Practice Graphing Linear Functions
Identify the y-intercept and the slope. Then, graph the function on graph paper.
- y = 5x + 1
y-intercept:
slope: - y = 10 - 3x
y-intercept:
slope: - y = -6 + 1x
y-intercept:
slope: - y = 5 - 2x
y-intercept:
slope: - y = 6 + -6x/25
y-intercept:
slope: - y = 32/15 + -16x/5
y-intercept:
slope: