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)Responsesb=15.71b equals 15.71b=12.29  b equals 12.29b=−5b equals negative 5b=11

Answer 1

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

\[ y = mx + b \]

Where:
- \( m \) is the slope (rate of change),
- \( b \) is the y-intercept,
- \( (x, y) \) is a point on the line.

Given:
- The slope \( m = -47 \)
- The point \( (14, 3) \)

We can plug these values into the equation to solve for \( b \):

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

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

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

\[
-47(14) = -658
\]

So now the equation becomes:

\[
3 = -658 + b
\]

3. Add 658 to both sides to solve for \( b \):

\[
b = 3 + 658
\]
\[
b = 661
\]

Thus, the initial value (y-intercept) of the linear function is \( b = 661 \).

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