How to Determine the Equation of a Line y = mx + b from a Graph

Step 1: Identify Two Points on the Line

Locate two distinct points on the line in the graph. Note down their coordinates as (x₁, y₁) and (x₂, y₂).

Step 2: Calculate the Slope m

Use the formula for slope m = (y₂ – y₁) / (x₂ – x₁) to find the slope of the line.

Step 3: Find the Y-Intercept b

Use one of the points and the slope to find the y-intercept b using the formula b = y – mx. You can use either (x₁, y₁) or (x₂, y₂) for this step.

Step 4: Write the Equation y = mx + b

Plug the values of m and b into the equation y = mx + b to get the equation of the line.

Summary

By following these steps, you can determine the equation of a line y = mx + b from its graph. This involves identifying two points on the line, calculating the slope, finding the y-intercept, and finally writing down the equation.