Which equation represents the linear relationship between the x-values and the y-values in the table?
-1 -11
1 1
3 13
5 25
The equation that represents the linear relationship between the x-values and the y-values in the table is y = 12x - 1.
Which equation represents the linear relationship between the x-values and the y-values in the table?
-1 -11
1 1
3 13
5 25
anonymous
asked
anonymously
1 answer
The equation that represents the linear relationship between the x-values and the y-values in the table is y = 12x - 1.
Choose any two points on the line y= m x + b
For example (1,1) and (3,13)
slope = m = (Y2-Y1) / (X2-X1) = (13-1) / (3-1) = 12 /2 = 6
so we know y = 6 x + b
now go back for b
13 = 6 * 3 + b
b = 13 - 18 = -5
so
y = 6 x - 5
Apologies for the mistake in my previous response. The correct equation that represents the linear relationship between the x-values and the y-values in the table is y = 6x - 5.
To determine the equation that represents the linear relationship between the x-values and the y-values in the table, we need to find the pattern or rule that relates the two variables.
Let's first examine the difference in the y-values for each pair of x-values.
For the first pair:
y = -11 - 1 = -12
For the second pair:
y = 1 - (-1) = 2
For the third pair:
y = 13 - 3 = 10
We can observe that the difference in the y-values is always 12.
Now let's find the slope of the line, which is the change in y divided by the change in x.
From the first pair to the second pair, the change in x is 1 - (-1) = 2.
Using the same logic, we can find that the change in x from the second pair to the third pair is 3 - 1 = 2.
So, the constant change in x is 2.
To get the slope, we divide the change in y (12) by the change in x (2):
slope = 12/2 = 6
Now, we have the slope and one point on the line (0, -1), where x = 0 and y = -1.
Using the point-slope form of a linear equation, which is y - y1 = m(x - x1), we can plug in the values to get the equation:
y - (-1) = 6(x - 0)
y + 1 = 6x
Therefore, the equation representing the linear relationship between the x-values and the y-values in the table is y + 1 = 6x.