MASS vs. VOLUME GRAPHS GRAPHING DENSITY FUNDAMENTALS - Quia
GRAPHING DENSITY FUNDAMENTALS: MASS vs. VOLUME GRAPHS
On these graphs, the axes represent the following: Y axis ? represents MASS on MASS VS. VOLUME GRAPHS X axis- represents VOLUME on MASS VS. VOLUME GRAPHS Slope of a line: refers to the "steepness" of a line (similar to the "steepness" of a hill/mountain) Slope of a line ? shows rate of change ? how much MASS changes as VOLUME changes Calculated by dividing RISE by RUN (change in Y AXIS divided by change in X AXIS):
Y ? X
*ON MASS/VOLUME GRAPHS. SLOPE REPRESENTS THE DENSITY OF THE SUBSTANCE! *WHY? BECAUSE SLOPE IS Y?X; ON A MASS/VOLUME GRAPH, Y = MASS, X = VOLUME, SO Y?X = MASS/VOLUME, WHICH = DENSITY!
CALCULATING SLOPE / DENSITY OF A LINE ON A MASS vs. VOLUME GRAPH
GOOD NEWS!!! Calculating slope can be easy! IF A LINE:
A. Is perfectly straight (no curves/angles) AND
B. passes through the origin (0, 0) Then its slope is calculated by picking ANY POINT and dividing its Y value by its X value. EXAMPLE: What is the slope of the line for substance 1?
Step 1: pick a point: let's choose this point: X (volume) = 2 mL, Y (mass) = 20 grams
Step 2: divide the Y value by the X value: 20 grams ? 2 mL = 10 grams/mL
So, the slope, and DENSITY, of substance 1 = 10 grams/mL
ANALYZING GRAPHS
1. STEEP SLOPES are lines that are NEARLY VERTICAL (straight up and down):
? these show HIGH RATES OF CHANGE: - on mass/volume graphs, they represent HIGH DENSITIES
2. GENTLE SLOPES are lines that are NEARLY HORIZONTAL (side to side):
? these show LOW RATES OF CHANGE: - on mass/volume graphs, they represent LOW DENSITIES
3. "ANGLES" IN THE LINE are CHANGING SLOPES - these show CHANGES IN THE RATE OF CHANGE -the more the line "bends", the greater the # of changes - MASS/VOLUME GRAPHS SHOULD NOT HAVE ANGLES. WHY?
ANALYSIS QUESTIONS: Use the graph provided to answer the following.
1a.Which SUBSTANCE has a greater density?
1b. what type of slope did you look for to determine your answer?
1c. using the fact that Density = slope = y ? x (for a straight line), calculate the density of this substance:
2a.Which SUBSTANCE has the lower density?
2b. what type of slope did you look for to determine your answer?
2c. using the fact that Density = slope = y ? x (for a straight line), calculate the density of this substance:
INTERPOLATING DATA USE THE LINES FOR EACH SUBSTANCE AND THE INFORMATION PROVIDED TO ANSWER THE FOLLOWING QUESTIONS:
3. ___ is the mass of 5 mL of substance 1
4.
is the
volume of 60 grams of
substance 2
5.
is the mass
of 4 mL of substance 2
6.
is the
volume of 40 grams of
substance 1
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