To write the equation in slope-intercept form \( y = mx + b \) using the points from the table, we first need to identify the slope (m) and the y-intercept (b).
From the provided points, let's choose two points to calculate the slope. We can use the points (0, 0) and (5, 5).
- Calculate the slope (m):
Using the formula for slope: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] where \((x_1, y_1) = (0, 0)\) and \((x_2, y_2) = (5, 5)\):
\[ m = \frac{5 - 0}{5 - 0} = \frac{5}{5} = 1 \]
- Identify the y-intercept (b):
The y-intercept (b) is the value of y when x = 0. From the point (0, 0), we see that \( b = 0 \).
Now we can write the equation in slope-intercept form:
\[ y = 1x + 0 \quad \text{or simply} \quad y = x \]
Therefore, the equation from the table is: \[ y = x \]