Questions: A verbal description of a linear function is given. Find the function. The linear function g has rate of change -1/9 and initial value 8/9. g(x)= Two points are given.

Solution Steps

To find the linear function \( g(x) \), we use the formula for a linear function, which is \( g(x) = mx + b \), where \( m \) is the rate of change (slope) and \( b \) is the initial value (y-intercept). Given that the rate of change is \(-\frac{1}{9}\) and the initial value is \(\frac{8}{9}\), we can directly substitute these values into the formula to find the function.

The formula for a linear function is given by \( g(x) = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

We are given the rate of change (slope) \( m = -\frac{1}{9} \) and the initial value (y-intercept) \( b = \frac{8}{9} \). Substituting these values into the linear function formula, we have: \[ g(x) = -\frac{1}{9}x + \frac{8}{9} \]

To find the value of the function at \( x = 0 \), substitute \( x = 0 \) into the equation: \[ g(0) = -\frac{1}{9}(0) + \frac{8}{9} = \frac{8}{9} \]

The value \(\frac{8}{9}\) can be expressed in decimal form as approximately \(0.8889\).

Final Answer