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.(1 point)
Responses
b=15.71
b equals 15.71
b=−5
b equals negative 5
b=12.29
b equals 12.29
b=11
To find the initial value (b) of the linear function, we can use the point-slope formula which states that the equation of a linear function can be written as y = mx + b, where m is the rate of change and b is the initial value.
Given that m = -47 and (14,3) is a point on the line, we can substitute these values into the equation to solve for b:
3 = -47(14) + b
Simplifying the equation:
3 = -658 + b
To isolate b, we can add 658 to both sides of the equation:
3 + 658 = b
661 = b
Therefore, the initial value (b) of the linear function is 661.
So, the correct answer is: b = 661.
To find the initial value (b) of the linear function, we can use the point-slope form of the equation:
y - y1 = m(x - x1)
where m is the rate of change and (x1, y1) is a point on the line.
In this case, the rate of change (m) is -47 and the given point is (14, 3).
Substituting these values into the equation, we get:
3 - y1 = -47(14 - x1)
Simplifying further:
3 - y1 = -658 + 47x1
Now, we can isolate b (the initial value) by moving the terms around:
y1 - 3 = 47x1 - 658
y1 - 3 + 658 = 47x1
y1 + 655 = 47x1
Dividing both sides by 47:
x1 = (y1 + 655)/47
Therefore, the initial value (b) is equal to (y1 + 655)/47, where y1 is the y-coordinate of the given point.
Since the given point is (14, 3), we substitute y1 = 3 into the equation:
b = (3 + 655)/47
b = 658/47
b ≈ 14
Therefore, the initial value of the linear function is approximately 14.
To find the initial value (b) of a linear function, you can use the formula: y = mx + b, where m is the rate of change and (x, y) is a point on the line.
In this case, the rate of change (m) is given as -47, and the point (14,3) lies on the line.
To find the initial value (b), substitute the given values into the formula and solve for b.
Using the point (14,3) in the formula, we get:
3 = -47 * 14 + b
Simplifying the equation gives:
3 = -658 + b
To isolate b, we add 658 to both sides of the equation:
b = 3 + 658
Simplifying further, we find:
b = 661
Therefore, the initial value (b) of the linear function is 661.