what's the equation for the table?
Answers
Answer:
y = -x/2 + 8 (or) x + 2y = 16.
Step-by-step explanation:
The general equation of a line will be of form y = mx + b, where m is the slope and b is the y-intercept.
Also we know that slope is defined as change in y/change in x = Δy/Δx.
Let us Compare two set of rows and see if we can find the slope
0 8
2 7 we can see that when x increased by 2, y decreased by 1.
---------------------------------------------------------------------------------------------------
2 7
3 6.5 we can see that when x increased by 1, y decreased by 0.5
----------------------------------------------------------------------------------------------------
3 6.5
10 3 we can see when x increased by 7, y decreased by 3.5
------------------------------------------------------------------------------------------------
If we now represent this in slope form you will see each of the above is represented as below,
Δy/Δx = - 1/2 ; Δy/Δx = - 0.5/1 = -1/2 ; Δy/Δx = - 3.5/7 = -1/2
Thus we find that in all cases Δy/Δx = - 1/2, which is the slope.
Hence the equation becomes y = (-1/2) x + b.
Now substitute x = 0, y = 8 in the equation y = (-1/2) x + b, to find out value of y-intercept, b.
y = (-1/2) x + b
=> 8 = (1/2)0 + b
=> b = 8.
Thus the equation becomes y = -x/2 + 8 (or) x + 2y = 16.
To further verify, you can substitute the remaining values of x and y given in table and this proves the equation is satisfied in all cases.