A straight‑line graph visually displays a mathematical function. The x‑ and y‑coordinates of points on the line reveal how two quantities relate. By determining the line’s slope (gradient) and its y‑intercept, you can translate this visual relationship into a clean algebraic formula.

Step 1: Locate the y‑Intercept

Find where the graph crosses the y‑axis. In this example, the intercept is at (0, 8).

Step 2: Choose a Second Point

Select any other point on the line. Here we’ll use (3, 2).

Step 3: Compute the Change in y

Subtract the first point’s y‑coordinate from the second’s: 8 – 2 = 6.

Step 4: Compute the Change in x

Subtract the first point’s x‑coordinate from the second’s: 0 – 3 = ‑3.

Step 5: Calculate the Slope

Divide the change in y by the change in x: 6 ÷ ‑3 = ‑2. This is the line’s slope (m).

Step 6: Write the Equation

Insert the slope and the y‑intercept into the slope‑intercept form, y = mx + c. Using our values, the equation becomes y = ‑2x + 8.