Question

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

Answer 1

`\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 = (y_2 -y_1)/(x_2 -x_1) = (54-2)/(1+2) = \frac{52}3 \\\\`

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