1. Exploring Linear Functions
3.1 Notes
Exploring Linear Functions

2. Positive Slope: Negative Slope:
As you read from left to right…the slope of the line goes up.
Negative Slope:
As you read from left to right…the slope of the line goes down.

3. Vertical Line x = # No Slope Horizontal Line y = # Slope is Zero

4. SLOPE-INTERCEPT FORM
y = mx + b
m = slope
b = y-intercept

5. Example: Find the slope and y-intercept of each line.
1) y = 3x + 1
Slope = 3
y-intercept = 1
2) y = 1/2x - 3
m = 1/2
b = -3

6. When graphing a line using an equation in slope-intercept form:
1 – Plot the y-intercept (b)
2 – Use the slope (m) as a fraction to plot a second point
Count up (+ slope) or down (- slope) according to the
numerator (rise) of the slope and right the number of spaces
indicated in the denominator (run) of the slope.
Slope =
Rise = m
Run
3 – Draw a line though the two points (don’t forget the arrows)

7. Example: Sketch the graph of the line.
3) y = -4x +2
Slope (m) = -4/1
Y-int (b) = 2

8. Example: Sketch the graph of the line.
4) y = 2/3x - 1
Slope (m) = 2/3
Y-int (b) = -1

9. Example: Is it a line? If so, write the next ordered pair.
To determine if a table is linear:
Check for consistent spacing between all x values and then all y values.
Example: Is it a line? If so, write the next ordered pair. +2 +2 +2 5) X 3 5 7 9 Y 10 4 1
YES; (11, -2) -3 -3 -3

10. Find the slope and y-intercept of the line. Label your answers.
Practice:
Find the slope and y-intercept of the line Label your answers.

11. 2) Identify the slope and y-intercept of each line
2) Identify the slope and y-intercept of each line. Then sketch the line.
y = -4x +2

12. Is it a line? If so, write the next ordered pair.3) X 1 2 3 Y 6 9 12 4) X 10 21 32 43 Y 5 12 20 29