Determine if the relationship represented in the table is linear. If it is linear, write an equation.
x|-2 5 7 10 12 20
y| 3 0 2 5 7 15
My answer is: Linear; y=x+ -5
Is this correct?
Thanks.
Q= Find the linear eq whose coordinate sum is 10 units
Ans-y=x+(-5)
Y=5
5=x+(-5)
X=-5-5
X=10
To determine if the relationship represented in the table is linear, we need to examine the changes in the y-values compared to the changes in the x-values.
Let's calculate the differences between consecutive x-values and the corresponding y-values:
x | -2 5 7 10 12 20
y | 3 0 2 5 7 15
Δy | -3 2 -3 2 8
From the differences between consecutive y-values (Δy column), we can see that the changes are not constant. In a linear relationship, the changes in the y-values would be the same for each unit increase in the x-values.
Since the changes in the y-values are not consistent, the relationship represented in the table is not linear.
Therefore, the equation you provided (y = x - 5) is not correct for this table since it assumes a linear relationship. We would need to use a different model to represent the given data accurately.