Question

Given that g(2) = 8 and g(5) = 512, what is the linear equation that defines g(x)?

a) g(x) = 168x - 328

b) g(x) = 152x - 296

c) g(x) = 168x - 296

d) g(x) = 152x - 328

Answer 1

The linear equation that defines g(x) is g(x) = 168x + 8.

Step-by-step explanation:

The linear equation that defines g(x) can be found using the given points (2, 8) and (5, 512).

First, we need to determine the slope (m) of the line. The slope is calculated by using the formula: m = (y2 - y1) / (x2 - x1).

Using the points (2, 8) and (5, 512), the slope is m = (512 - 8) / (5 - 2) = 168.

Next, we can use the point-slope form of a linear equation, which is y - y1 = m(x - x1), and substitute one of the given points into the equation along with the slope to find the y-intercept (b).

Using the point (2, 8), we have: 8 - 8 = 168(2 - 2) + b, which simplifies to b = 8.

Therefore, the linear equation that defines g(x) is: g(x) = 168x + 8.