I NEED TO WRITE AN EQUATION TO REPRESENT THE FOLLOWING FUNCTION
INPUT X 1 2 3 4 5
OUTPUT Y 2 6 10 14 18
PLEASE HELP THIS IS MAKING US CRAZY
1 2
2 6
3 10
4 14
5 18
it looks like for every increase of 1 in the x
there is an increase of 4 in the y
so we have a relation of
y = 4x
BUT, notice if x = 1, I would get 4 , not 2 like we should
so how about
y = 4x - 2
test it for the other values.
To write an equation that represents the given function, we need to determine the pattern between the input (X) and output (Y) values.
Looking at the output values, we can observe that they increase by a constant difference of 4. This suggests that the function has a linear relationship.
To find the equation, we can use the slope-intercept form of a linear equation: y = mx + b, where m is the slope and b is the y-intercept.
First, let's calculate the slope (m). We can take any two sets of points from the table:
Using (1, 2) and (2, 6):
m = (y2 - y1) / (x2 - x1)
m = (6 - 2) / (2 - 1)
m = 4 / 1
m = 4
Next, we can substitute the values of one point (let's use x = 1 and y = 2) and the slope into the equation to find the y-intercept (b):
2 = 4(1) + b
2 = 4 + b
b = 2 - 4
b = -2
Therefore, the equation that represents the given function is:
y = 4x - 2
To write an equation that represents the given function, we need to determine the relationship between the input (X) and the output (Y) values.
Looking at the pattern, we can observe that the output values are increasing by 4 each time the input value increases by 1. So, the relationship between X and Y is linear, with a constant rate of change of 4.
To find the equation, we can use the slope-intercept form of a linear equation, which is given by:
Y = mx + b
Where:
- Y represents the output value
- X represents the input value
- m represents the slope (the rate of change)
- b represents the y-intercept (the value of Y when X = 0)
To find the slope (m), we can choose any two points from the table. Let's choose (1, 2) and (2, 6):
m = (Y2 - Y1) / (X2 - X1)
= (6 - 2) / (2 - 1)
= 4 / 1
= 4
Now, we need to find the y-intercept (b). We can use the equation and substitute the values of any point. Let's use (1, 2):
2 = 4(1) + b
Simplifying the equation:
2 = 4 + b
b = 2 - 4
b = -2
Therefore, the equation that represents the given function is:
Y = 4X - 2
That is the equation you are looking for.