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.

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.

Transcript text: 4. [-/5 Points] DETAILS MY NOTES SCOLALGCC1CR 2.2.036 A verbal description of a linear function is given. Find the function. The linear function $g$ has rate of change $-\frac{1}{9}$ and initial value $\frac{8}{9}$. $g(x)=$ $\square$ [-/5 Points] DETAILS MYNOTES SCOLALGCC1CR 2.3.036.EP. Two points are given.

Solution

Solution Steps

Solution Approach

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.

Step 1: Identify the Linear Function Formula

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

Step 2: Substitute Given Values

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: \[ g(x) = -\frac{1}{9}x + \frac{8}{9} \]

Step 3: Evaluate the Function at $ x = 0 $

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

Step 4: Convert to Decimal Form

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