Question

Find the initial value of the linear function, given that the rate of change is m equals negative Start Fraction 4 over 7 End Fraction, and left parenthesis 14 comma 3 right parenthesis is an left parenthesis x comma y right parenthesis value of the linear function.

Answer 1

To find the initial value of the linear function, we need to use the point-slope form of a linear equation.

The point-slope form of a linear equation is:

y - y1 = m(x - x1)

Where:
m = rate of change = -4/7
(x1, y1) = (14, 3)

Plugging in the values, we get:

y - 3 = -4/7(x - 14)

Now, we need to simplify the equation to slope-intercept form (y = mx + b), where b is the initial value.

y - 3 = -4/7x + 56/7
y = -4/7x + 56/7 + 3

y = -4/7x + 56/7 + 21/7
y = -4/7x + 77/7
y = -4/7x + 11

Therefore, the initial value of the linear function is 11.