To write the equation in slope-intercept form (y = mx + b), we first need to determine the slope (m) and the y-intercept (b) from the data provided in the table.
Let's first analyze the points given in the table:
- (0, 0)
- (3, 3)
- (-2, -2)
- (1, 1)
- (-4, -4)
- (-1, -1)
- (-6, -6)
- (-3, -3)
From observing these points, we can see a clear linear relationship. It appears that as \( x \) increases, \( y \) increases proportionally.
To calculate the slope \( m \) between two points, we can use the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Let's take two points from the table: (0, 0) and (3, 3).
Here, \( (x_1, y_1) = (0, 0) \) and \( (x_2, y_2) = (3, 3) \).
So,
\[ m = \frac{3 - 0}{3 - 0} = \frac{3}{3} = 1 \]
Now, we also notice that when \( x = 0 \), \( y = 0 \) which indicates that the y-intercept \( b = 0 \) as well.
Thus, we have:
- Slope \( m = 1 \)
- Y-intercept \( b = 0 \)
Now we can write the equation in slope-intercept form:
\[ y = 1x + 0 \]
This simplifies to:
\[ y = x \]
Therefore, the equation from slope-intercept form is:
\[ y = x \]