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)

Question

Responses

b=12.29

b=15.71

b=11

b=−5

Answer 1

To find the initial value (b) of the linear function in the slope-intercept form \( y = mx + b \), we can use the given information:

1. The slope \( m = -\frac{4}{7} \)
2. The point \( (14, 3) \), meaning when \( x = 14 \), \( y = 3 \)

We can plug these values into the slope-intercept equation:

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

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

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

Now substitute this back into the equation:

\[ 3 = -8 + b \]

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

\[ b = 3 + 8 = 11 \]

Therefore, the initial value of the linear function is:

\[ \boxed{11} \]