x = 2 , 4 , 6 , 8
y = 18, 34, 50, 66
This is supposed to be a table where the x lines up with the y in order
How would I find the equation to solve this when x = 20?
x goes up by +2
y goes up by +16 but starts with 18
The relationship is
y = 2 + 8 x
if x = 18, y = 146
Also, how did you come up with the equation?
Where did the 8 and 2 come from?
I understand now
Good.
8 was the obvious slope.
I picked the constant term 2 so that any one of the (x,y) combinations would match.
To find the equation to solve for the value of y when x = 20, we can observe the pattern in the given data points.
Here, we have a constant rate of change for both x and y.
For x, it increases by +2 with each step: 2, 4, 6, 8, ...
For y, it increases by +16 with each step but starts with 18: 18, 34, 50, 66, ...
To find the equation, we can use the slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept.
Let's find the slope (m):
The slope is the change in y divided by the change in x. Since the change in y is +16 and the change in x is +2, we can calculate the slope:
m = (change in y) / (change in x) = 16 / 2 = 8
Now, let's find the y-intercept (b):
To do this, we can substitute one of the points from the table into the equation and solve for b. Let's use the point (2, 18) to calculate b:
y = mx + b
18 = 8(2) + b
18 = 16 + b
b = 18 - 16
b = 2
Now we have the slope (m = 8) and the y-intercept (b = 2).
So, the equation that relates x and y in this case is:
y = 8x + 2
To find the value of y when x = 20, we can substitute x = 20 into the equation:
y = 8(20) + 2
y = 160 + 2
y = 162
Therefore, when x = 20, y equals 162.