Question

Write the linear equation that gives the rule for this table.

X Y
3 -5
4 -10
5 -15
6 -20

Answer 1

To find the linear equation that describes the relationship between \( X \) and \( Y \) in the given table, we can start by identifying the slope (m) of the line.

Looking at the values:

- When \( X = 3 \), \( Y = -5 \)
- When \( X = 4 \), \( Y = -10 \)
- When \( X = 5 \), \( Y = -15 \)
- When \( X = 6 \), \( Y = -20 \)

Notice that as \( X \) increases by 1, \( Y \) decreases by 5. Thus, the slope \( m \) is:

\[
m = \frac{\Delta Y}{\Delta X} = \frac{-5}{1} = -5
\]

Now we can use the slope and one of the points to find the equation in the slope-intercept form \( Y = mX + b \).

Using the point \( (3, -5) \):

\[
-5 = -5(3) + b
\]
\[
-5 = -15 + b
\]
\[
b = -5 + 15 = 10
\]

Now we have the slope \( m = -5 \) and the y-intercept \( b = 10 \). Therefore, the linear equation that describes the table is:

\[
Y = -5X + 10
\]