Find the initial value of the linear function, given that the rate of change is m=−4/7

Question

, and (14,3)
is an (x,y)
value of the linear function.(1 point)
Responses

b=12.29
b equals 12.29

b=11
b equals 11

b=−5
b equals negative 5

b=15.71

Answer 1

To find the initial value \( b \) of the linear function, we can use the slope-intercept form of the equation of a line, which is given by:

\[ y = mx + b \]

where \( m \) is the rate of change (slope) and \( b \) is the y-intercept (initial value).

Given the slope \( m = -\frac{4}{7} \) and the point \( (14, 3) \), we can substitute these values into the equation to solve for \( b \).

1. Substitute \( m \), \( x \), and \( y \) into the equation: \[ 3 = -\frac{4}{7}(14) + b \]

2. Calculate \( -\frac{4}{7}(14) \): \[ -\frac{4 \times 14}{7} = -\frac{56}{7} = -8 \]

3. Now, plug this back into the equation: \[ 3 = -8 + b \]

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

So the initial value \( b \) is \( 11 \).

The correct response is:

b = 11.