Find the initial value of the linear function, given that the rate of change is

Question

m = -4/7, and (14, 3) is an (x, y) value of the linear function. (1 point)
B =-5
• b = 12.29
• B= 11
• b = 15.71

Answer 1

To find the initial value (b) of the linear function in the form \(y = mx + b\), we can use the rate of change \(m = -\frac{4}{7}\) and the point \((14, 3)\) given.

We can substitute \(m\), \(x\), and \(y\) into the equation to solve for \(b\):

1. Start with the equation:
   \[ y = mx + b \]

2. Substitute the values:
   \[ 3 = -\frac{4}{7} \cdot 14 + b \]

3. Now, calculate \(-\frac{4}{7} \cdot 14\):
   \[ -\frac{4}{7} \cdot 14 = -\frac{56}{7} = -8 \]

4. Substitute back into the equation:
   \[ 3 = -8 + b \]

5. Solve for \(b\):
   \[ b = 3 + 8 = 11 \]

The initial value \(b\) of the linear function is 11.

So the correct answer is: B = 11.