A linear relation is a relationship between two variables that when the corresponding pair of values of the variables are plotted, a straight line is obtained
The equation for the relationship between hours Gwen worked and number of tickets is <u> t = </u><u>15·h</u>
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The reason the above equation is correct is as follows:
The given parameters are;
The table of values;
Hours(h): 1, 2, 3, 4
Tickets (t): 15, 30, 45, 60
Required: To write an equation that gives the relation between the number of hours Gwen worked and the number of tickets sold
Solution:
From the given table, we have;
The common difference between successive <em>h-values </em>is 1
The <em>common difference</em> between successive t<em>-values </em>is 30 - 15 = 45 - 30 = 60 - 45 = 15 = Constant
Given that the common difference of the <em>h</em>, and <em>t-values</em> are constant, the relationship is a linear relationship of the form, t = m·h + c
Where;
m = The rate of change of <em>t</em> with <em>h</em>, as follows;
m = (30 - 15)/(2 - 1) = 15
∴ t - 15 = 15 × (h - 1)
t - 15 = 15·h - 15
t = 15·h - 15 + 15 = 15·h
t = 15·h
The equation for the relation between the number of hours Gwen worked and the number of tickets she sold is<u> t = </u><u>15·h</u>
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