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.
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.
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.
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.