A table contains the ordered pairs (3, 42.25) and (5, 50.75). If the relationship in the table is linear, explain how to find the initial value. make the writing short

Answer 1

To find the initial value (y-intercept) of a linear relationship defined by the ordered pairs (3, 42.25) and (5, 50.75), follow these steps:

1. Determine the slope (m) using the formula:
   \( m = \frac{y_2 - y_1}{x_2 - x_1} \)
   For the points (3, 42.25) and (5, 50.75):
   \( m = \frac{50.75 - 42.25}{5 - 3} = \frac{8.5}{2} = 4.25 \)

2. Use the slope-intercept form of a line:
   \( y = mx + b \)
   Plug in one of the points to solve for b (the y-intercept). Using (3, 42.25):
   \( 42.25 = 4.25(3) + b \)
   Simplifying gives:
   \( 42.25 = 12.75 + b \)
   \( b = 42.25 - 12.75 = 29.5 \)

The initial value (y-intercept) is 29.5.