Question

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

\[
\boxed{11}
\]