To find the rate of change, we can calculate the difference in the values of Y divided by the difference in the values of X.
Rate of change = (Y2 - Y1) / (X2 - X1)
= (8 - 4) / (-3 - 1)
= 4 / -4
= -1
The rate of change of the linear function is -1.
To find the initial value, we can use the formula for a linear function:
Y = mx + b
Plugging in the values of X and Y from the table:
4 = 1m + b (for X=1, Y=4)
8 = -3m + b (for X=-3, Y=8)
We can solve these equations simultaneously to find the values of m and b.
By solving the first equation, we get:
4 = 1m + b
b = 4 - m
Substitute b = 4 - m into the second equation:
8 = -3m + 4 - m
8 = -4m + 4
4 = -4m
m = -1
Now that we have found the value of m, we can find b:
b = 4 - (-1)
b = 4 + 1
b = 5
Therefore, the linear function given as a table of values is:
Y = -1x + 5
Use the table to answer the question
X Y
1 4
-3 8
Find the rate of change and the initial value of the linear function given as a table of values
1 answer