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I-06: Graphs, slopes and basic laboratory data

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Module I-06 · Recommended before: Before interpreting experimental figures

Graphs, slopes and basic laboratory data

Graphs show relationships among variables. Slope measures vertical change divided by horizontal change; units are y-axis units per x-axis unit.

Learn the method

slope = (y₂ − y₁)/(x₂ − x₁)

  1. Read axes, units and scales first.
  2. Identify two valid points on the line.
  3. Calculate Δy/Δx.
  4. Retain units on the slope.
  5. Describe the physical meaning, not only the arithmetic.

Common mistake: Do not reverse rise and run; a slope has units.

Worked example

Problem: A line goes through (0 mL, 0 g) and (10 mL, 20 g). What is the slope?

Step-by-step solution: (20−0) g / (10−0) mL = 2.0 g/mL, which can represent density.

Check the units and whether the answer is reasonable before continuing.

More applications of this mathematics

Try each extension before expanding its solution.

Mean and spread

Measurements 1.1, 1.2, 1.3 g have mean 1.2 g. The sample standard deviation is 0.10 g; do not confuse it with the range (0.2 g).

Calibration graph

If A = 0.40c + 0.02 and absorbance A = 0.22, then concentration c = (0.22−0.02)/0.40 = 0.50 in the calibration concentration units.

Independent practice — five questions

Suggested mastery threshold: four out of five. Incorrect answers display a worked explanation after submission.

Choose one response for each question, then select “Check my answers.” No timer. Hints are optional. You can retry freely. Questions are formative, not proctored.

Question 1. What is the slope of the line through (0 mL, 0 g) and (6 mL, 18 g)?
Hint for question 1

Slope is rise divided by run.

Question 2. What is the slope of the line through (0 mL, 0 g) and (7 mL, 28 g)?
Hint for question 2

Slope is rise divided by run.

Question 3. What is the slope of the line through (0 mL, 0 g) and (8 mL, 24 g)?
Hint for question 3

Slope is rise divided by run.

Question 4. What is the slope of the line through (0 mL, 0 g) and (9 mL, 36 g)?
Hint for question 4

Slope is rise divided by run.

Question 5. What is the slope of the line through (0 mL, 0 g) and (10 mL, 40 g)?
Hint for question 5

Slope is rise divided by run.

Supporting reference

OpenStax Chemistry 2e / NIST — reference for this subject. This lesson’s wording, examples and questions are original.

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