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 and write it like an 8th grader

Answer 1

To find the initial value of a linear relationship, follow these steps:

1. Identify the Ordered Pairs: We have the points (3, 42.25) and (5, 50.75). Here, the first number is the input (x) and the second number is the output (y).

2. Find the Slope (m): The slope tells us how much y changes for each change in x. Use the formula:

   \[ m = \frac{y2 - y1}{x2 - x1} \]

   Plug in the points: \[ m = \frac{50.75 - 42.25}{5 - 3} = \frac{8.5}{2} = 4.25 \]

3. Write the Equation: Now use the slope and one of the points (let's say (3, 42.25)) to write the equation in the slope-intercept form:

   \[ y = mx + b \] Substitute the slope (m = 4.25) and the point (3, 42.25):

   \[ 42.25 = 4.25(3) + b \]

4. Solve for b (initial value): Now calculate it: \[ 42.25 = 12.75 + b \] \[ b = 42.25 - 12.75 = 29.5 \]

So, the initial value (b) is 29.5. This means when x is 0, y would be 29.5!