I need help! I am supposed to complete the table and write an equation to show the relationship. The table has input of x, 0,1,2,3,4,5 and output of y,4,10,16,22,and the last two outputs are blank. I think they are 28 and 34--but what is the relationship?
the realationship is the pattern the is between all of the numbers
I think the answer is....x=0.5 and y=1
To find the relationship between the input (x) and the output (y), let's look for a pattern in the given data. In this case, we can observe that the output (y) increases by 6 each time the input (x) increases by 1.
Here's a step-by-step explanation to complete the table and find the equation:
1. Start with the given input-output pairs:
x: 0, 1, 2, 3, 4, 5
y: 4, 10, 16, 22
2. Observe the pattern: As x increases by 1, y increases by 6.
3. Complete the table by continuing the pattern:
x: 0, 1, 2, 3, 4, 5
y: 4, 10, 16, 22, 28, 34
4. To write an equation that represents the relationship between x and y, we can use the slope-intercept form of a linear equation, y = mx + b, where m represents the slope and b represents the y-intercept.
Since the output (y) increases by 6 every time the input (x) increases by 1, the slope (m) is 6.
5. Now we need to find the y-intercept (b). To do this, we can use any given input-output pair from the table. Let's choose x = 0, y = 4.
Substituting these values into the equation, we get:
4 = 6(0) + b
4 = b
Therefore, the y-intercept (b) is 4.
6. Now that we have the slope (m = 6) and the y-intercept (b = 4), we can write the equation:
y = 6x + 4
So, the relationship between the input (x) and the output (y) is described by the equation y = 6x + 4.