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Module 3B1: Getting the Equation for a Straight Line

1

The concentration of calcium in a solution can be determined by measuring the intensiy of light emitted in a flame photometer.

Given the following data, write the equation for the line.

Concentration (μM) Reading
2 0.40
4 0.71
6 1.01
8 1.3
10 1.6
12 1.9


y = x +

well done

incorrect.

Choose two points on the line, say (2, 0.4) and (12, 1.9)

The slope is (1.9-0.4)/(12-2) = 0.15

The y-intercept is y - mx = 0.4 - 0.15x2 = 0.1

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2

Following on from question 1, if the reading of an unknown sample was 1.2, estimate its concentration

Calcium concentration of unknown sample = μM

well done

incorrect

Rearrange the equation to make x the subject

x = (y - 0.1)/0.15

substitute in y = 1.2

x = 1.1/0.15 = 7.3 μM

two significant figures are justified here.

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3

Given the following data, find the equation for the line.

x y
5 5.98
10 5.55
15 5.12
20 4.7
25 4.28
30 3.85


y = x +

well done

incorrect

Choose two points on the line

say (10, 5.55) and (20, 4.7)

the slope is = (5.55-4.7)/(10-20)

= 0.85/-10

=-0.085

the y intercept is 5.55 - (-0.085x10)

=5.55 + 0.85

=6.4

the equation is y = -0.085x + 6.4

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4

Following on from the previous question, if the value for y = 4.8, what is the corresponding value for x?

x = (two significant figures is appropriate here)

well done

incorrect

the equation is y = 6.4 - 0.085x

rearrange to make x the subject

x = (y-6.4)/-0.085

substitute in for y = 4.8

x = (4.8-6.4)/-0.085

x = 18.8 = 19 to 2 significant figures

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