The height of the candle after 9 hours can be written as 23.4 cm.
The linear relationship is the relationship between two variables such that it follows a straight line.
As it is given that the height of the candle is linear to the amount of time. Now, let's the time be on the x-axis and the y-axis be the height of the candle. therefore, the slope of the linear relationship can be represented as,
Point1 of the slope, (x₁, y₁) = (6, 24.6)
Point2 of the slope, (x₂, y₂) = (21, 18.6)
Now, since we know the two points of the linear relationship, therefore, the slope can be written as,
[tex]m = \dfrac{y_2-y_1}{x_2-x_1}\\\\m = \dfrac{18.6-24.6}{21-6}\\\\m = \dfrac{-6}{15}\\\\m = -0.4[/tex]
Thus, the slope of the linear relationship is -0.4.
Now, the equation of the linear relationship can be written as,
[tex]y = mx+C\\\\y_1 = mx_1+C\\\\24.6= (-0.4 \times 6) + C\\\\24.6 = -2.4 +C\\\\C = 27[/tex]
Thus, the Linear relationship of the candle height and the amount of time can be written as [tex]y=-0.4x+c[/tex].
Now, In order to calculate the height of the candle after 9 hours, we will substitute the value of the x as 9.
[tex]y=-0.4x+27\\\\y=-0.4(9)+27\\\\y = -3.6 + 27\\\\y = 23.4[/tex]
Hence, the height of the candle after 9 hours can be written as 23.4 cm.
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