x: -2, -1, 0, 1, 2
y: 9, 4, -1, -6, -11
What is the function rule?
note that y decreases by 5 for each increase of 1 in x.
So, y = -5x + b
since y(0) = -1,
y = -5x-1
this doesnt make sense. can you explain it better steve
Doesn't this make sense to you??
Steve said, "y decreases by 5 for each increase of 1 in x."
when i calulated the function rule he gave it didnt make sense. Ms. Sue, whats the function rule, thats all i wanna know
To find the function rule that relates the values of x and y, we need to look for a pattern in the given data.
Looking at the values of x and y, we can see that as x increases by 1, y decreases by 5. This suggests that there is a linear relationship between x and y.
To determine the function rule, we can use the formula for the equation of a straight line: y = mx + c, where m is the slope of the line and c is the y-intercept.
To find the slope (m), we can use any two data points. Let's choose the first and last points:
Using the points (-2, 9) and (2, -11), we can calculate the slope (m) using the formula:
m = (y₂ - y₁) / (x₂ - x₁)
m = (-11 - 9) / (2 - (-2))
m = -20 / 4
m = -5
Now we need to find the y-intercept (c). We can choose any point on the line to determine the y-intercept. Let's use the point (0, -1):
Using the slope-intercept form (y = mx + c), we can substitute the values we have and solve for c:
-1 = -5(0) + c
-1 = c
Now we have the slope (m = -5) and the y-intercept (c = -1).
Substituting these values into the slope-intercept form, we get the function rule:
y = -5x - 1
Therefore, the function rule is y = -5x - 1.