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=12.29
b equals 12.29

b=−5
b equals negative 5

b=15.71
b equals 15.71

b=11
b equals 11

Answer 1

To find the initial value (y-intercept) \( b \) of a linear function given the slope \( m \) and a point \( (x_0, y_0) \), we can use the slope-intercept form of a linear equation:

\[
y = mx + b
\]

We can plug in the values we have:
- The slope \( m = -\frac{4}{7} \)
- The point \( (14, 3) \): here \( x_0 = 14 \) and \( y_0 = 3 \).

Substituting these values into the equation, we get:

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

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

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

Now, our equation becomes:

\[
3 = -8 + b
\]

To solve for \( b \), add 8 to both sides:

\[
b = 3 + 8 = 11
\]

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

Therefore, the correct response is:

**b = 11** or **b equals 11**.