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
A) Linear; y = x - -5
B) Linear; y = -5x
C) Linear; y = x + -5
D) Not linear
I'm thinking it's C am I correct
Correct!
Can you please explain to me why it's C I just guessed it
To determine if the relationship represented in the table is linear, we need to check if the differences between consecutive x-values and y-values are constant.
Let's calculate the differences between consecutive x-values:
5 - 2 = 3
7 - 5 = 2
10 - 7 = 3
12 - 10 = 2
20 - 12 = 8
The differences between consecutive x-values are not the same; they are not constant. Therefore, the relationship is not linear.
So, the correct answer is D) Not linear.
To determine if the relationship represented in the table is linear, we can check if there is a constant rate of change between the values of x and y.
First, let's calculate the difference between consecutive x-values:
5 - 2 = 3
7 - 5 = 2
10 - 7 = 3
12 - 10 = 2
20 - 12 = 8
Now, let's calculate the difference between consecutive y-values:
0 - (-3) = 3
2 - 0 = 2
5 - 2 = 3
7 - 5 = 2
15 - 7 = 8
If the differences between the x-values and y-values are consistent, then the relationship is linear.
Looking at the differences, we see that both the differences between the x-values and the differences between the y-values are consistent (3, 2, 3, 2). Therefore, the relationship is linear.
To find the equation of the line, we can use the slope-intercept form: y = mx + b
Let's use the point (2, -3) to find the value of b:
-3 = 2m + b
Now, let's use the point (5, 0) to find the value of m:
0 = 5m + b
We can solve these two equations to find the slope-intercept equation.
-3 = 2m + b
0 = 5m + b
By eliminating b, we can subtract the second equation from the first equation:
-3 - 0 = 2m - 5m + b - b
-3 = -3m
Dividing both sides of the equation by -3:
m = 1
Now, substituting the value of m into one of the original equations:
0 = 5(1) + b
0 = 5 + b
b = -5
Therefore, the equation for the linear relationship is y = x - 5.
So the correct answer is A) Linear; y = x - 5.