use the table to answer the question.
heres the table:
x y
2.6 -6
3.2 3
determine the rate of change of the linear function given as a table of values.
A: m= 0.067
B: m= -15
C: m= 15
D: m= -5
To determine the rate of change of the linear function given as a table of values, we can calculate the slope of the line connecting the two points.
The formula for slope (m) is:
m = (y2 - y1) / (x2 - x1)
Using the given values from the table:
x1 = 2.6, y1 = -6
x2 = 3.2, y2 = 3
Substituting these values into the formula:
m = (3 - (-6)) / (3.2 - 2.6)
= (3 + 6) / (0.6)
= 9 / 0.6
= 15
Therefore, the rate of change of the linear function is 15.
The correct answer is C: m = 15.
find the initial value of the linear function, given that the rate of change is m= -4/7 and (14,3) is an (x,y) value of the linear function.
A: b= 15.71
A: b=-5
C: b= 11
D: b= 12,29
To find the initial value of the linear function, we can use the formula:
y = mx + b
Where y and x are the coordinates of a point on the line, m is the rate of change, and b is the initial value.
We know that the rate of change (m) is -4/7 and one point on the line is (14,3).
Substituting these values into the formula:
3 = (-4/7)(14) + b
To solve for b, we first simplify the right side expression:
3 = -8 + b
Next, we isolate b by adding 8 to both sides of the equation:
b + 8 + 8 = -8 + 8 + b
b + 8 = 0 + b
The expression on the left side simplifies to:
b + 8 = b
Since the b variable is isolated on one side, we can conclude that b = 8.
Therefore, the initial value of the linear function is b = 8.
The correct answer is not provided in the options given.
find the initial value of the linear function, given that the rate of change is m= -4/7 and (14,3) is an (x,y) value of the linear function.
A: b= 15.71
A: b=-5
C: b= 11
D: b= 12.29
To find the initial value of the linear function, we can use the formula:
y = mx + b
Where y and x are the coordinates of a point on the line, m is the rate of change, and b is the initial value.
We know that the rate of change (m) is -4/7 and one point on the line is (14,3).
Substituting these values into the formula:
3 = (-4/7)(14) + b
To simplify the right side expression, we can multiply -4/7 by 14:
3 = -8 + b
Next, we isolate b by adding 8 to both sides of the equation:
3 + 8 = -8 + 8 + b
11 = b
Therefore, the initial value of the linear function is b = 11.
The correct answer is C: b = 11.