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=−5
b equals negative 5

b=11
b equals 11

b=12.29
b equals 12.29

b=15.71

Answer 1

To find the initial value (the y-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:

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

We can substitute the values into the equation to find \( b \):

1. Substitute \( m \), \( x \), and \( y \) into the equation:

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

2. Calculate \( -\frac{4}{7}(14) \):

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

3. Now substitute back into the equation:

   \[ 3 = -8 + b \]

4. Solve for \( b \):

   \[ b = 3 + 8 = 11 \]

So the y-intercept (initial value) \( b = 11 \).

The correct response is:

b equals 11