Find the rate of change and the initial value of the linear function given as these values: (1,4) (-3,8)

Answer 1

The slope, or rate of change, of a linear function can be found using the formula:

m = (y₂ - y₁) / (x₂ - x₁)

Using the values (1,4) and (-3,8) in this formula, we get:

m = (8 - 4) / (-3 - 1)
= 4 / (-4)
= -1

So, the rate of change of the linear function is -1.

To find the initial value, also known as the y-intercept, we can use the slope-intercept form of a linear function, which is:

y = mx + b

Using the values (1,4) and the slope (m) of -1, we can substitute these values into the equation to solve for b:

4 = -1(1) + b
4 = -1 + b
4 + 1 = b
b = 5

So, the initial value of the linear function is 5.

Therefore, the linear function can be expressed as:
y = -x + 5