To solve this problem, we need to find the equation of the line that represents the second table and the intersection point of the two lines.
Given the equation [tex]\( y = -\frac{1}{3}x + 7 \)[/tex] for the first line, we can start by finding the equation for the line that uses points from the second table.
1. Select two points from the second table to find the slope and intercept:
- Using points: (-6, 9) and (-3, 8)
2. Calculate the slope ([tex]\( m \)[/tex]):
- The formula for slope is: [tex]\( m = \frac{y_2 - y_1}{x_2 - x_1} \)[/tex]
- Plugging in the points: [tex]\( m = \frac{8 - 9}{-3 - (-6)} = \frac{-1}{3} = -\frac{1}{3} \)[/tex]
3. Calculate the y-intercept (\ c \)) for the line:
- Use the point (0, 7): [tex]\( y = mx + c \rightarrow 7 = -\frac{1}{3}(0) + c \rightarrow c = 7 \)[/tex]
Thus, the equation for the second line is: [tex]\( y = \frac{1}{3}x + 7 \)[/tex]
To find the intersection point:
1. Set the two equations equal to each other:
- [tex]\(-\frac{1}{3}x + 7 = \frac{1}{3}x + 7\)[/tex]
2. Solving for [tex]\( x \)[/tex]:
- Combine like terms: [tex]\(-\frac{2}{3}x = 0\)[/tex]
- [tex]\( x = 0 \)[/tex]
3. Plug [tex]\( x \)[/tex] back into either equation to find [tex]\( y \)[/tex]:
- Using: [tex]\( y = -\frac{1}{3}(0) + 7 \rightarrow y = 7 \)[/tex]
Therefore, the other equation is [tex]\( y = \frac{1}{3}x + 7 \)[/tex], and the solution to the system is [tex]\( (0, 7) \)[/tex].
So the completed answer is:
The equation that represents the other equation is [tex]\( y = \frac{1}{3} x+7 \)[/tex].
The solution of the system is [tex]\( (0, 7) \)[/tex].
