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 given in the table.
Let's analyze the pairs from the table:
- \((0, -3)\)
- \((5, -2)\)
- \((10, -7)\)
- \((15, -12)\)
Step 1: Calculate the slope \(m\)
The slope \(m\) can be calculated using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Let's choose two points from the table. We'll use \((0, -3)\) and \((5, -2)\):
\[ m = \frac{-2 - (-3)}{5 - 0} = \frac{-2 + 3}{5} = \frac{1}{5} \]
Step 2: Determine the y-intercept \(b\)
We can use the y-intercept directly from the point \((0, -3)\). Here, when \(x = 0\), \(y = -3\), thus \(b = -3\).
Step 3: Write the equation
Using the slope \(m = \frac{1}{5}\) and the y-intercept \(b = -3\), we can now write the equation:
\[ y = \frac{1}{5}x - 3 \]
Conclusion
The equation in slope-intercept form from the provided table is:
\[ y = \frac{1}{5}x - 3 \]