Find the initial value of the linear function, given that the rate of change is m = −4 over 7 , and (14,3) is an (x,y) value of the linear function.

Question

options:

b=11
b equals 11

b=15.71
b equals 15.71

b=−5
b equals negative 5

b=12.29

Answer 1

To find the initial value (b) of the linear function given the slope (m) and a specific point (x, y), we can use the slope-intercept form of the equation of a line:

\[ y = mx + b \]

We are given:

• The rate of change \( m = -\frac{4}{7} \)
• A point \( (14, 3) \)

Now, substitute the given values into the equation:

1. Substitute \( y = 3 \), \( m = -\frac{4}{7} \), and \( x = 14 \):

\[ 3 = -\frac{4}{7}(14) + b \]

2. Calculate \( -\frac{4}{7}(14) \):

\[ -\frac{4 \cdot 14}{7} = -\frac{56}{7} = -8 \]

3. Now replace this into the equation:

\[ 3 = -8 + b \]

4. Solve for \( b \):

\[ b = 3 + 8 \] \[ b = 11 \]

Thus, the initial value \( b \) is 11.

The correct option is:

• b = 11 (or b equals 11)