Question

find the rate of change and the initial value of the linear function given as these values: (-4,-10/+3) (-1,-4/+3)

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the rate of change and the initial value of a linear function, we can use the formula for the slope of a line:

slope (rate of change) = (change in y)/(change in x)

Using the given values (-4, -10/+3) and (-1, -4/+3), we can calculate the rate of change as follows:

Rate of change = (change in y)/(change in x) = ((-10/+3) - (-4/+3))/((-4) - (-1))

Simplifying this expression, we get:

Rate of change = (-10/+3 + 4/+3)/(-4 + 1) = (-6/+3)/(-3) = -2

Therefore, the rate of change of the linear function is -2.

To find the initial value, we can use the point-slope form of a linear equation:

y - y1 = m(x - x1)

where (x1, y1) is one of the given points. Let's use the point (-4, -10/+3):

y - (-10/+3) = -2(x - (-4))

Simplifying this expression, we get:

y + 10/+3 = -2(x + 4)

Multiplying through by 3 to eliminate the fraction, we have:

3y + 10 = -6(x + 4)

Expanding the expression on the right side, we get:

3y + 10 = -6x - 24

To isolate y, we subtract 10 and divide through by 3:

3y = -6x - 34

y = (-6x - 34)/3

Therefore, the initial value of the linear function is -34/3.