1. Graphical Relationships Objectives –Learn graphing skills and understand graphical relationships

2. Graphing What makes a proper Graph? –A coordinate system Origin, defined and labeled Data Points, instructions on how they are defined Axes, defined, labeled, which way is increasing, units used 0 Displacement (m) Time (s) P (t 1, d 1 ) Q (t 2, d 2 ) t1t1 t2t2 d1d1 d2d2

3. Graphical Relationships Y Does NOT Depend on X (Scatter Diagram) A = proportional relationship B = inversely proportional relationship C = no relationship D = nonlinear 0 X Y

4. Graphical Relationships A = proportional relationship B = inversely proportional relationship C = no relationship D = nonlinear 0 X Y

5. Proportional Relationship As X increases, Y increases As X decreases, Y decreases 0 X Y

6. Graphical Relationships A = proportional relationship B = inversely proportional relationship C = no relationship D = nonlinear 0 X Y

7. Inversely Proportional Relationship As X increases, Y decreases As X decreases, Y increases 0 X Y

8. Graphical Relationships A = proportional relationship B = inversely proportional relationship C = no relationship D = nonlinear (quadratic or exponential) 0 X Y

9. Graphing Independent Variable: Experimenter Controls Dependent Variable: Measurement Interval (x-axis)  x = x 2 - x 1 Interval (y-axis)  y = y 2 - y 1 0 Dependent Variable Independent Variable P (x 1, y 1 ) Q (x 2, y 2 ) x1x1 x2x2 y1y1 y2y2 yy

10. Graphing Slope = rate of change = rise/run =  y/  x 0 Y X x1x1 x2x2 y1y1 y2y2 yy xx

11. Pathagoras and Right Triangles c 2 = a 2 + b 2 b a c c = hypotenuse = side opposite the right angle slope = rise/run = a/b

12. Density   = m/V mass =  Volume 0 Volume (cm 3 ) Mass (grams) Water Ice Lead

13. Density  mass =  Volume Y = slope X slope is the density, the relationship between mass and volume, the rate of change of mass with volume. 0 Volume (cm 3 ) Mass (grams) Water Ice Lead

14. Density  mass =  Volume A 10 cm 3 volume of which substance would weigh the least? 0 Volume (cm 3 ) Mass (grams) Water Ice Lead

15. Density  mass =  Volume A 5 gram mass of which substance would occupy the smallest volume? 0 Volume (cm 3 ) Mass (grams) Water Ice Lead