Question

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 it short

Answer 1

To find the initial value of a linear relationship given two ordered pairs (x₁, y₁) and (x₂, y₂), follow these steps:

1. **Calculate the slope (m)** using the formula:
\[
m = \frac{y₂ - y₁}{x₂ - x₁}
\]
For the pairs (3, 42.25) and (5, 50.75):
\[
m = \frac{50.75 - 42.25}{5 - 3} = \frac{8.5}{2} = 4.25
\]

2. **Use the point-slope form** of the linear equation:
\[
y - y₁ = m(x - x₁)
\]
Choose one of the points, for example, (3, 42.25):
\[
y - 42.25 = 4.25(x - 3)
\]

3. **Convert to slope-intercept form (y = mx + b)** to find the initial value (b):
\[
y = 4.25x - 12.75 + 42.25 \implies y = 4.25x + 29.5
\]

Thus, the initial value (y-intercept) is **29.5**.