Input s ? ? 9 12 15
t 70 66 62 58 54
Write the rule as an equation. Use the
equation to extend your pattern.
3, 6..They are increasing by 3
Bottom row is decreasing by 4
Can't figure out the answer either need the equation explaining the relationship between s & t
To write the rule as an equation, we need to determine the relationship between the variables s and t.
Looking at the pattern, we can observe that s decreases by 3 each time, and t decreases by 4 each time. This suggests a linear relationship between s and t.
Using the information given, we can see that:
s: 9 → 12 → 15
t: 70 → 66 → 62 → 58 → 54
First, let's find the equation for the relationship between s and t. We can use the formula for the equation of a straight line, which is y = mx + b, where y represents t, x represents s, m represents the slope, and b represents the y-intercept.
To find the slope (m), we can use the formula:
m = (change in t) / (change in s)
For every change in s (which is 3), t decreases by 4. So:
m = -4 / 3
Now, we need to find the y-intercept (b). We can pick any point from the pattern and substitute the corresponding values of s and t into the equation. Let's choose the first point (9, 70):
70 = (-4/3)(9) + b
Simplifying the equation:
70 = -12 + b
b = 70 + 12
b = 82
Now we have the values of m and b:
m = -4/3
b = 82
We can write the equation for the relationship between s and t:
t = (-4/3)s + 82
To extend the pattern, we can plug in new values for s into the equation and solve for t. For example, if we want to find t when s is 18, we substitute s = 18 into the equation:
t = (-4/3)(18) + 82
Simplifying the equation:
t = -24 + 82
t = 58
Therefore, when s is 18, t is 58, according to the equation.