Use the table to answer the question.

Question

x y
2.6 −6
3.2 3

Determine the rate of change of the linear function given as a table of values.
(1 point)
Responses

m=−5
m equals negative 5
m=0.067
m equals 0.067
m=−15
, m equals negative 15
m=15
m equals 15

Answer 1

m = 3 - (-6) / 3.2 - 2.6 = 9/0.6 = 15

Therefore, the rate of change of the linear function is m = 15.

Answer 2

Find the initial value of the linear function, given that the rate of change is m=−47, and (14,3) is an (x,y) value of the linear function.(1 point)
Responses

b=−5
b equals negative 5
b=12.29
, b equals 12.29
b=15.71
b equals 15.71
b=11

Answer 3

Using the point-slope form of a linear equation:

y - y1 = m(x - x1)

where m is the rate of change and (x1, y1) is a point on the line.

Substituting m = -47, x1 = 14 and y1 = 3, we get:

y - 3 = -47(x - 14)

Expanding the right-hand side and rearranging, we get:

y = -47x + 665

Comparing this with the slope-intercept form y = mx + b, we see that the initial value is b = 665.

Therefore, the initial value of the linear function is b = 665.