Do the data in the table represent a linear function? If so, write a rule for the function.
x: –3 –2 –1 0 1
y: 1 –2 –5 –8 –11
yes; y = –3x – 8
yes; y = 1/3x – 8
yes; y = 1/3x + 8
yes; y = 3x + 8
I think I know the answer to this one. I studied each of the choices to find the one that fit the problem.
What do you think?
I think it is "yes; y = –3x – 8"
Yay! I agree!
Thanks!
You're welcome.
To determine if the data in the table represents a linear function, we need to check if there is a constant rate of change between the x and y values. In other words, we need to check if the change in y is proportional to the change in x.
Let's calculate the rate of change between the x and y values:
From x = -3 to x = -2, the change in y is 1 - (-2) = 3.
From x = -2 to x = -1, the change in y is -2 - (-5) = 3.
From x = -1 to x = 0, the change in y is -5 - (-8) = 3.
From x = 0 to x = 1, the change in y is -8 - (-11) = 3.
As we can see, the change in y is always 3 for a change in x of 1. This means that there is a constant rate of change between the x and y values, which makes the data in the table represent a linear function.
To find the rule for the function, we can use the slope-intercept form of a linear equation, which is y = mx + b. Here, m represents the slope (rate of change) and b represents the y-intercept (the value of y when x = 0).
From the data, we can see that the slope (m) is -3 because for every 1 unit increase in x, y decreases by 3 units. And the y-intercept (b) is -8 because when x = 0, y = -8.
So the rule for the function is: y = -3x - 8. Hence, the correct answer is: yes; y = -3x - 8.