Which of the following equations gives the relationship between S and T in the table below?

S 1 2 3 4 5 6

T 1 4 7 10 13 16

How do you find equations again?

slope = (13-10)/(5-4) for example

= 3
so
T = = 3 S + b
1 = 3 + b
b = -2
so
T = 3 S - 2

Wait! Nevermind, figured it out! Use linear equation right?

Oh, finding equations is like trying to solve a mystery! It's all about observing the pattern and playing detective with numbers. Now, looking at the table, it seems like the T column increases by 3 each time. So, if we let S represent the number in the S column, we can say that the equation is T = 3S - 2. Ta-daa! We cracked the case!

To find the equation that gives the relationship between S and T in the given table, you need to observe the pattern in the values of S and T. Here's how you can do it step-by-step:

Step 1: Look at the difference between consecutive values of T. Calculate the differences between each value of T: 3 (4-1), 3 (7-4), 3 (10-7), 3 (13-10), 3 (16-13).

Step 2: Observe the pattern in the differences. In this case, the differences between consecutive values of T are constant (3 in this example). This suggests that the relationship between S and T is likely linear.

Step 3: Determine the value of T when S is zero. Looking at the table, when S is 0, T is 0 as well. This indicates that the y-intercept (the value of T when S is zero) is 0.

Step 4: Write the equation of the line. Now that we know the constant difference between T values (3) and the y-intercept (0), we can write the equation of the line in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. In this case, the equation is T = 3S.

Therefore, the equation that gives the relationship between S and T in the table is T = 3S.

To find the equation that represents the relationship between the variables S and T, we can look for a pattern or trend in the given table. In this case, the values of S increase by increments of 1, while the values of T increase by increments of 3.

To convert this pattern into an equation, we can start by determining the initial value or constant term. Looking at the table, when S is 1, T is also 1. Therefore, the equation should include a term that is equivalent to 1 when S is 1.

Next, we need to consider the rate of change or the slope of the equation. Looking at the table, we can see that for every increment of 1 in S, T increases by 3. This means that the slope of the equation should be 3.

Putting all the information together, we can write the equation as follows:

T = 3S + 1

In this equation, S represents the input values and T represents the corresponding output values. The equation states that to find T, we multiply the value of S by 3, and then add 1 to the result.