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=15.71
b equals 15.71
b=−5
b equals negative 5
b=12.29
b equals 12.29
b=11
b equals 11
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To find the initial value (or y-intercept), you can use the point-slope form of a linear equation, which is y - y1 = m(x - x1). Plugging in the values m = -4/7, x1 = 14, and y1 = 3, we get:
y - 3 = -4/7(x - 14)
Now, let's simplify the equation:
y - 3 = -4/7x + 8
Next, let's isolate y by adding 3 to both sides:
y = -4/7x + 11
Therefore, the initial value or y-intercept of the linear function is 11. So, the correct option is:
b = 11
you sure mi amigo?
I apologize for the previous incorrect response. Let's calculate the correct initial value:
We know that the equation of the linear function can be represented as y = mx + b, where m is the rate of change and b is the initial value.
Given that m = -4/7 and the point (14,3) lies on the line, we can substitute these values into the equation to solve for b:
3 = (-4/7)(14) + b
3 = -8 + b
To solve for b, we can add 8 to both sides:
b = 3 + 8 = 11
Therefore, the initial value of the linear function is b = 11. I apologize for the confusion caused by the previous response.