How to Graph Line in Slope Intercept Form

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, wherem 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.More »

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.More »

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: