Question

Initial value and rate of change for the points -3,2.5 0,1 and 2,0

Answer 1

To find the initial value and rate of change for the points given, we can use the formula for the slope of a line, which is:

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

Point 1: (-3, 2.5)
Point 2: (0, 1)

m = (1 - 2.5) / (0 - (-3))
m = (-1.5) / 3
m = -0.5

The initial value (y-intercept) can be found by substituting one of the points into the equation of a line:

y = mx + b

Using point (-3, 2.5):

2.5 = -0.5(-3) + b
2.5 = 1.5 + b
b = 1

Therefore, the equation of the line passing through points (-3, 2.5) and (0, 1) is:

y = -0.5x + 1

The initial value is 1 and the rate of change is -0.5

Point 1: (0, 1)
Point 2: (2, 0)

m = (0 - 1) / (2 - 0)
m = -1 / 2
m = -0.5

The initial value can be found using the equation of a line:

y = mx + b

Using point (0, 1):

1 = -0.5(0) + b
1 = b

Therefore, the equation of the line passing through points (0, 1) and (2, 0) is:

y = -0.5x + 1

The initial value is 1 and the rate of change is -0.5.