To write an equation in slope-intercept form (y = mx + b), we first need to determine the slope \( m \) and the y-intercept \( b \) using the data provided in the table.
From the table, we have the following points:
- (0, 2)
- (5, -3)
- (10, -8)
- (15, -13)
Step 1: Calculate the slope (m)
The formula for the slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Let's use the points (0, 2) and (5, -3):
- \( (x_1, y_1) = (0, 2) \)
- \( (x_2, y_2) = (5, -3) \)
Now plug in the values:
\[ m = \frac{-3 - 2}{5 - 0} = \frac{-5}{5} = -1 \]
Step 2: Calculate the y-intercept (b)
The y-intercept \( b \) is the value of \( y \) when \( x = 0 \). From the first point (0, 2), we see that when \( x = 0 \), \( y = 2 \). Therefore, \( b = 2 \).
Step 3: Write the equation
Now that we have the slope \( m = -1 \) and the y-intercept \( b = 2 \), we can write the equation in slope-intercept form:
\[ y = -1x + 2 \]
or simply:
\[ y = -x + 2 \]
This is the equation that represents the data from the table.