Answer:
y = -3x + 10
where y = Value and x = Position
or
Value = - 3(Position) + 10
Explanation:
We can determine a linear equation for this table in slope-intercept form
The slope intercept form of a linear equation is
y = mx + b
y is referred to as the dependent variable and x the independent variable
Here m is the slope which is the rate of change of y with respect to x
b = y-intercept which is the value of y when x = 0
For the given table it appears that the value is dependent on the position
So the independent variable, let's call it x, is position
The dependent variable, y, is value
Plugging values of x, y into the generalized equation
y = mx + b
At x(position) = 1, we get y = 7
==> 7 = m(1) + b
==> 7 = m + b
== m + b = 7 ............................. (1)
At x = 3, y = 1
==> 1 = m(3) + b
==> 1 = 3m + b
==> 3m + b = 1 ..............................(2)
If we subtract equation 1 from equation (2) we get
(3m + b) - (m + b) = 1 - 7
3m - m + b - b = -6
2m + 0 = -6
2m = -6
m = -6/2 = -3
So we now know m = -3 we can write the equation as
y = -3m + b
To find b, plug in any value of x and corresponding y from the table and solve for b. remember that x is position and y is value
Let's choose the last entry x = 9, y = -17
Plugging these into y = -3x + b gives
-17 = -3(9) + b
-17 = -27 + b
Switch sides:
- 27 + b = -17
Add 27 to both sides:
- 27 + 27 + b = -17 + 27
b = 10
So the equation for the table is
y = - 3x + 10
or in terms of the table
Value = - 3(Position) + 10
You can check this is correct by choosing a value for position from the table and seeing the equation value is consistent with the given value