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.

Answer 1

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.

Answer 2

To find the initial value of the linear function, we can use the formula for a linear function:

y = mx + b

where m is the slope (rate of change) and b is the initial value.

We are given that the rate of change is m = -47. Plugging in this value, we have:

3 = (-47)(14) + b

To find b, we can solve for it:

3 = -658 + b

Adding 658 to both sides:

3 + 658 = b

661 = b

Therefore, the initial value of the linear function is 661.

Answer 3

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

y = mx + b

where m is the slope and b is the initial value.

We are given that the rate of change (slope) is m = -4/7. Plugging in this value and the given point (14, 3), we have:

3 = (-4/7)(14) + b

To find b, we can solve for it:

3 = (-4/7)(14) + b

Multiplying -4/7 by 14 gives:

3 = -8 + b

Adding 8 to both sides:

3 + 8 = b

11 = b

Therefore, the initial value (intercept) of the linear function is 11.