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Artist 52 [7]
2 years ago
7

Let f(x)=(18)3^x. find the equation of the line between the points (-2,f(-2)) and (1,f(1))

Mathematics
1 answer:
horsena [70]2 years ago
6 0

\text{Given that,} \\\\f(x) = 18 \cdot 3^x \\\\f(-2) = 18 \cdot 3^{-2} = 2\\\\f(1) = 18 \cdot 3^1 = 54\\ \\\text{So,}~ (x_1,y_1) = (x_1, f(-2)) = (-2,2) ~\text{and}~ (x_2,y_2) = (x_2, f(1)) = (1,54)\\ \\\text{Slope,}~ m = \dfrac{y_2 -y_1}{x_2 -x_1} = \dfrac{54-2}{1+2} = \dfrac{52}3 \\\\

\text{Equation of line,}\\\\~~~~~~~y - y_1 = m (x-x_1)\\\\\\\implies y-2 = \dfrac{52}3(x+2)~~~~~~~~~~~;[\text{Point-Slope form.]} \\\\\\\implies y-2 = \dfrac{52}3x + \dfrac{104}3\\\\\\\implies y = \dfrac{52}{3}x + \dfrac{104} 3 +2\\\\\\\implies y = \dfrac{52}3 x +\dfrac{110}3 ~~~~~~~~~~~~~~~;[\text{Slope -Intercept form}]

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We are given

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now, we will check each options

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so, this is TRUE

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option-C:

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