To find the initial value of the linear function, we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
where m is the rate of change and (x1, y1) is a point on the line.
Using the given rate of change m = -4/7 and the point (14,3), we can substitute these values into the equation:
3 - y1 = (-4/7)(14 - x1)
Next, we need to solve for y1 (the initial value). We can simplify the equation:
3 - y1 = (-4/7)(14 - x1)
3 - y1 = (-4/7)(14) + (4/7)(x1)
3 - y1 = -8/7 + (4/7)(x1)
3 - y1 = (4/7)(x1) - 8/7
To isolate y1, we can subtract (4/7)(x1) and add 8/7 to both sides:
3 - y1 - (4/7)(x1) + 8/7 = 0
Multiplying both sides of the equation by 7 to eliminate the fractions, we get:
21 - 7y1 - 4(x1) + 8 = 0
Simplifying further:
29 - 7y1 - 4(x1) = 0
To find the initial value y1, we need to set x1 = 0:
29 - 7y1 - 4(0) = 0
29 - 7y1 = 0
-7y1 = -29
y1 = -29/-7
y1 = 29/7
y1 = 4.14
So the initial value of the linear function is approximately y1 = 4.14.
Therefore, the correct response is b = 4.14.
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) Responses b=−5 b equals negative 5 b=12.29 b equals 12.29 b=15.71 b equals 15.71 b=11
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