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=15.71
b equals 15.71

b=11
b equals 11

b=−5
b equals negative 5

b=12.29

Answer 1

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

\[ y = mx + b \]

Here, \( m \) is the slope of the line, \( (x, y) \) is a point on the line, and \( b \) is the y-intercept (the initial value).

Given:

• Rate of change \( m = -\frac{4}{7} \)
• Point \( (14, 3) \)

We can substitute the values of \( x \), \( y \), and \( m \) into the equation to find \( b \):

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

First, calculate \( -\frac{4}{7} \times 14 \):

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

Now substitute this back into the equation:

\[ 3 = -8 + b \]

To solve for \( b \):

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

Thus, the initial value \( b \) is:

\[ \boxed{11} \]