Question

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=15.71
b equals 15.71

b=−5
b equals negative 5

b=11

Answer 1

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

\[ y = mx + b \]

where:
- \( y \) is the output (y-value),
- \( m \) is the slope (rate of change),
- \( x \) is the input (x-value),
- \( b \) is the y-intercept (initial value).

We are given:
- Slope \( m = -\frac{4}{7} \)
- A point \( (x, y) = (14, 3) \)

We can substitute \( m \), \( x \), and \( y \) into the equation to solve for \( b \):

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

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

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

Now substitute this into the equation:

\[ 3 = -8 + b \]

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

\[ b = 3 + 8 = 11 \]

Therefore, the initial value \( b = 11 \).

So the answer is:

**b=11**