Question

(-1, -4/3) (-4, -10/3) Determine the initial value and the rate of change of the linear function as given in the graph.

Answer 1

To determine the initial value and rate of change of the linear function, we can use the slope-intercept form of a linear equation, which is given by:

y = mx + b

where m is the rate of change (slope) and b is the initial value (y-intercept).

Given the points (-1, -4/3) and (-4, -10/3), we can find the rate of change (m) by using the formula:

m = (y2 - y1) / (x2 - x1)

Where (x1, y1) = (-1, -4/3) and (x2, y2) = (-4, -10/3).

m = (-10/3 - (-4/3)) / (-4 - (-1))
m = (-10/3 + 4/3) / (-4 + 1)
m = (-6/3) / (-3)
m = 2/1
m = 2

So, the rate of change of the linear function is 2.

To find the initial value (b), we can substitute one of the given points into the equation y = mx + b. Let's use (-1, -4/3).

-4/3 = 2(-1) + b
-4/3 = -2 + b
b = -4/3 + 2
b = -4/3 + 6/3
b = 2/3

So, the initial value of the linear function is 2/3.

Therefore, the linear function is y = 2x + 2/3.