Plssss help mee
input Output
1 9
2 12
3 15
Is the relationship linear? Why or why not?
did you notice:
12-9=3
15-12=3
so what is your verdict ?
linear means that the change in y is a constant multiple of the change in x. So, going from point to point, make a table of the changes.
x-change y-change
1 3
1 3
so, the change in y is always 3 times the change in x. So, yes, the relationship is linear:
y = 3x+6
Thank you so much ^^
To determine if the relationship between the input and output is linear, we need to check if there is a constant rate of change between each input and its corresponding output. In a linear relationship, the output increases or decreases by the same amount for each unit increase in the input.
Let's calculate the rate of change for this relationship by subtracting each output value from the previous one:
Output1 - Output0 = 9 - 0 = 9
Output2 - Output1 = 12 - 9 = 3
Output3 - Output2 = 15 - 12 = 3
As we can see, the rate of change between the input values is not constant. Initially, the rate is 9, then it decreases to 3. This indicates that the relationship is not linear because the output values do not increase or decrease by the same amount for each unit increase in the input.
Therefore, the relationship described by the given input and output values is not linear.