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
(1 point)
yes; y = –3x – 8
yes; y = 1/3x – 8
yes; y = 1/3x + 8
yes; y = 3x + 8
1.C
2B
3 D
4D
5D
6D
7 B
100%
y=-(3x+8) that should be it
Thank you so very much for helping me on the questions that I am struggling with.
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.
Let's examine the changes in y for each unit change in x:
From x = -3 to x = -2: y changes from 1 to -2, a decrease of 3.
From x = -2 to x = -1: y changes from -2 to -5, a decrease of 3.
From x = -1 to x = 0: y changes from -5 to -8, a decrease of 3.
From x = 0 to x = 1: y changes from -8 to -11, a decrease of 3.
We can see that for every increase of 1 in x, y decreases by 3. This constant rate of change indicates a linear relationship.
Now, let's write a rule for the function. We observe that the initial value of y is 1 when x = -3, and the rate of change is -3 (for every increase of 1 in x, y decreases by 3). Using the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept, we can substitute the values:
y = -3x + b
To find b, we can substitute the values of x and y when x = -3 and y = 1:
1 = -3(-3) + b
1 = 9 + b
b = 1 - 9
b = -8
Therefore, the rule for the function is:
y = -3x - 8.
So, the correct answer is:
Yes; y = -3x - 8.