To find the correct system of equations to represent the two tables, we need to determine the equations for the lines represented by the data in each table.
Table 1:
x | y
-------
1 | 3
2 | 4
3 | 5
4 | 6
5 | 7
By examining Table 1, we can see that as \( x \) increases by 1, \( y \) increases by 1 as well. This indicates a linear relationship with a slope of 1. The y-intercept when \( x = 0 \) appears to be 2 (since when \( x = 1 \), \( y = 3 \)). Thus, the equation for Table 1 can be derived as:
\[ y = x + 2 \]
Table 2:
x | y
-------
1 | 6
2 | 3
3 | 0
4 | -3
5 | -6
In Table 2, as \( x \) increases by 1, \( y \) decreases by 3. Therefore, the slope is -3. To find the y-intercept, we can use the point \( (1, 6) \) and plug it into the slope-intercept form \( y = mx + b \):
\[ 6 = -3(1) + b \implies b = 6 + 3 = 9 \]
Thus, the equation for Table 2 is:
\[ y = -3x + 9 \]
Now we have the equations:
- From Table 1: \( y = x + 2 \)
- From Table 2: \( y = -3x + 9 \)
Looking at the answer choices, we find that:
- Answer choice (a) is correct: \[ y = x + 2 \quad (Table 1) \] \[ y = -3x + 9 \quad (Table 2) \]
Thus, the answer is (a): \( y = x + 2 \) and \( y = -3x + 9 \).
3 answers