The Slope of a Line… Continued! From tables and more graphing

Focus 7 - Learning Goal #1: The student will understand the connections between proportional relationships, lines, and linear equations and use functions to model relationships between quantities. 4 3 2 1 In addition to level 3.0 and beyond what was taught in class, the student may: Make connection with other concepts in math. Make connection with other content areas.   The student will demonstrate and explain the connections between proportional relationships, lines, and linear equations and use functions to model relationships between quantities. The student will demonstrate and identify proportional relationships, lines, and linear equations and use functions to model quantities. With help from the teacher, the student has partial success with level 2 and 3 elements. Even with help, students have no success with level 2 and 3 content.

Review important things about slope… Slope is a fraction of the change in y over change in x. Slope is represented by the letter m Vertical line has NO slope (it’s undefined) Horizontal line has a slope zero (it’s 0) change in y change in x

Formula for slope:

Review Finding the slope of a line passing through points (-7,3) and (-1,-2) -2 - 3 -5 m = = -1 - -7 6

Find the slope (or rate of change) shown in the table To Find Slope from a Table: Find the slope (or rate of change) shown in the table 1. Select any two points from the table Let’s use (0,6) and (4,9) (x1,y1) (x2,y2) Now find slope from the points like normal 2. Assign the first point as (x1,y1) and assign the second point as (x1,y1) 3. Use slope formula 9 - 6 3 4. Plug values in and simplify m = = 4 - 0 4

Find the slope (or rate of change) shown in the table Let’s use (-2,8) and (0,0) 0 - 8 -8 m= = = -4 0 - -2 2

To Graph a Line Given a Point and the Slope: Plot the single point that is provided From that point, count how many units up or down from the numerator of the slope (top of fraction). If slope is positive (+) move up, if slope is negative (–) move down. Then count how many units over to the right from the denominator of the slope (bottom of fraction) Plot a new point there, repeat to plot another point, and connect the dots to draw a straight line. 1 (-3,6) m= Put a point on (-3,6), then the slope of 1/2 means go up 1, over right 2 to draw the next point 2

Graph the line passing through (3, 1) with slope 2. Plot the point (3, 1). The slope is 2, write that as a fraction 2/1 . So for every 2 units up, you will move right 1 unit. 2. Then move 2 units up and right 1 unit and plot the point (4, 3). 3. Repeat. Use a straightedge to connect the points. 1 2 (3, 1)

Graph the line passing through (1, 1) with slope -3. The slope is -3, or the fraction -3/1 . So for every 3 units down, you will move right 1 unit (1, 1) 1. Plot the point (1, 1). 2. Then move 3 units down and right 1 unit and plot the point (2,-2). 3. Use a straightedge to connect the two points. 3 1