Use the table to answer the 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
m = 3 - (-6) / 3.2 - 2.6 = 9/0.6 = 15
Therefore, the rate of change of the linear function is m = 15.
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
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.
To determine the rate of change of the linear function given as a table of values, we need to calculate the slope of the line connecting the given points (x1, y1) and (x2, y2).
Using the formula:
m = (y2 - y1) / (x2 - x1)
Let's plug in the values from the table:
For the first point, (x1, y1) = (2.6, -6)
For the second point, (x2, y2) = (3.2, 3)
Now, let's calculate the slope:
m = (3 - (-6)) / (3.2 - 2.6)
m = 9 / 0.6
m = 15
Therefore, the rate of change of the linear function given by the table of values is m = 15.