3 1 Notes Exploring Linear Functions Positive Slope

3. 1 Notes Exploring Linear Functions

Positive 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.

Vertical Line x = # No Slope X = -6 y=5 Horizontal Line y = # Slope is Zero

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

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

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)

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

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

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 5) X Y 3 5 10 7 7 -3 +2 +2 9 4 -3 1 -3 YES; (11, -2)

Practice: 1) Find the slope and y-intercept of the line. Label your answers.

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

Is it a line? If so, write the next ordered pair. 3) 4) X 0 1 2 3 Y 3 6 9 12 X 10 21 32 43 Y 5 12 20 29