Write a function rule for:
x 1 2 3 4 5
y 1 5 9 13 17
I do not get these please explain?
note that y increases by 4 when x increases by 1.
So, expect something like y=4x.
But 4*1 = 4, not 1, so subtract 3.
y = 4x-3
Looks good to me.
That is what I got. Thank you
To find a function rule for the given data, we need to analyze the relationship between the variables x and y. Looking at the given values, we can observe that:
x: 1 2 3 4 5
y: 1 5 9 13 17
From this data, we can see that the y-values increase by 4 each time the x-value increases by 1. This indicates a linear relationship between x and y.
To find the equation for this linear relationship, 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.
Let's calculate the slope (m) first. The slope is the rate at which the y-values change for each unit increase in x.
m = (change in y)/(change in x) = (y₂ - y₁)/(x₂ - x₁) = (5 - 1)/(2 - 1) = 4/1 = 4.
Now, to find the y-intercept (b), we can choose any point from the given data (x, y). Let's pick the point (1, 1):
1 = 4(1) + b
1 = 4 + b
b = 1 - 4
b = -3.
Therefore, the function rule for the given data is:
y = 4x - 3.
So, for any given value of x, you can substitute it into the equation y = 4x - 3 to find the corresponding value of y.