Question

Find the initial value of the linear function, given that the rate of change is m=−47 , 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=12.29 b equals 12.29 b=−5

Answer 1

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

\[
y = mx + b
\]

Here, \( m \) is the slope (rate of change) and \( (x, y) \) is a point on the line. We can rearrange this equation to solve for \( b \) using the provided point \( (14, 3) \) and the slope \( m = -47 \).

Using the point \( (14, 3) \):

1. Substitute \( y = 3 \), \( m = -47 \), and \( x = 14 \) into the equation:

\[
3 = -47(14) + b
\]

2. Calculate \( -47(14) \):

\[
-47 \times 14 = -658
\]

3. Now substitute that value back into the equation:

\[
3 = -658 + b
\]

4. To solve for \( b \), add 658 to both sides:

\[
b = 3 + 658
\]

5. Therefore,

\[
b = 661
\]

Given the options you've provided, it seems there might be a misunderstanding as we arrived at 661, which is not one of the choices. Please double-check the values given or the slope to ensure everything is correct, or let me know if there is any additional information.