To write a linear equation in the form \( y = mx + b \), we first need to identify the values given in the table. The table has the points:
- When \( x = 0 \), \( y = 8 \)
- When \( x = 5 \), \( y = -10 \)
- When \( x = 10 \), \( y = -28 \)
We can use any two points to calculate the slope \( m \) and then use one of the points to solve for \( b \) (the y-intercept).
Let's use the points \( (0, 8) \) and \( (5, -10) \).
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 given by:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Using the points \( (0, 8) \) and \( (5, -10) \):
- \( x_1 = 0, y_1 = 8 \)
- \( x_2 = 5, y_2 = -10 \)
\[ m = \frac{-10 - 8}{5 - 0} = \frac{-18}{5} = -\frac{18}{5} \]
Step 2: Solve for the y-intercept (b)
Using the slope-intercept form \( y = mx + b \) and the point \( (0, 8) \):
\[ 8 = -\frac{18}{5}(0) + b \] \[ b = 8 \]
Step 3: Write the Linear Equation
Now, we can write the equation of the line:
\[ y = -\frac{18}{5}x + 8 \]
This is your linear equation in the form of \( y = mx + b \).
Therefore, the final answer is:
\[ y = -\frac{18}{5}x + 8 \]