x: -2,-1, 0, 1, 2
-------------------
y: 9, 4,-1,-6,-11
find the function rule. please??
Ouch, there is a small typo in the previous message. Here is the correct one:
1) Draw the function on a piece of paper
It is a linear function, is not it?
So, the function will have the form:
y = ax+b
where a and b- coefficients
2) look at the value of the function at x=0, it is -1:
-1=a*0+b
b=-1
3) if you move b on the left side, you will get direct dependence of new y on x:
y+1=ax
and since you know the values of the function:
x: -2,-1, 0, 1, 2
-------------------
y-1: 10, 5,0,-5,-10
now it is easy:
y(-2)=10=-2*a
a=-5
4) So, finally you get y = -5x-1
Another way to find the function is to paste the values into excel :D
1) Draw the function on a piece of paper
It is a linear function, is not it?
So, the function will have the form:
y = ax+b
where a and b- coefficients
2) look at the value of the function at x=0, it is -1:
-1=a*0+b
b=-1
3) if you move b on the left side, you will get direct dependence of new y on x:
y+1=ax
and since you know the values of the function:
x: -2,-1, 0, 1, 2
-------------------
y-1: 10, 5,0,-5,-10
now it is easy:
y(-2)=10b
b=-5
or
y(-1)=5b
b=-1
4) So, finally you get y = -5x-1
Another way to find the function is to to paste the values into excel :D
Thank you so much you went into detail and actually helped me understand unlike any of the actual lessons.
To find the function rule, we need to observe the relationship between the values of x and y in the given set.
Looking at the values, we can see that each y-coordinate is decreasing by 5 as the x-coordinate increases by 1. This suggests that the function rule is linear and can be expressed as y = mx + b, where m is the slope and b is the y-intercept.
To determine the slope (m), we can select any two pairs of coordinates and use the formula:
m = (y2 - y1) / (x2 - x1)
Let's choose the pairs (-2, 9) and (-1, 4):
m = (4 - 9) / (-1 - (-2))
m = -5 / 1
m = -5
So, the slope (m) of our linear function is -5.
Next, we can find the y-intercept (b) by substituting the values of one of the points and the calculated slope (m) into the equation y = mx + b and solve for b.
Using the first point (-2, 9):
9 = (-5)(-2) + b
9 = 10 + b
b = 9 - 10
b = -1
Therefore, the function rule that represents the relationship between x and y is:
y = -5x - 1