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
Y=2X+12
Y=5X-6
Y=6X-5
Y=-X-11
Y=2X+12
y = 6 x - 5
Apologies, but the correct equation representing the linear relationship between the x-values and y-values in the table is:
Y = 6X - 5
To determine which equation represents the linear relationship between the x-values and the y-values in the table, we can use the slope-intercept form of a linear equation: y = mx + b. In this form, m represents the slope of the line and b represents the y-intercept.
Let's find the slope first:
To find the slope (m), we can use the formula:
m = (change in y) / (change in x)
Using the given table, we can calculate the change in y and change in x for any two points.
For example, let's calculate the slope using the first two points (-1, -11) and (1, 1):
change in y = 1 - (-11) = 12
change in x = 1 - (-1) = 2
So, the slope between these two points is:
m = 12 / 2 = 6
Now that we have the slope, let's find the y-intercept (b).
To find the y-intercept, we can substitute one of the points (let's use (-1, -11)) and the slope (m) into the slope-intercept form of the equation y = mx + b, and solve for b:
-11 = 6 * (-1) + b
-11 = -6 + b
Adding 6 to both sides:
-11 + 6 = b
-5 = b
Therefore, the equation representing the linear relationship between the x-values and the y-values in the table is:
Y = 6X - 5.
So the correct answer is Y = 6X - 5.