By Mary Freeman

Updated Aug 30, 2022

Linear equations form the backbone of algebra and all higher mathematics. When plotted on a Cartesian plane, they produce a straight line described by the formula y = mx + b, where m is the slope and b the y‑intercept.

Instructions

Step 1 – Identify the Standard Form

Start with the canonical equation:

y = mx + b

Here, m represents the slope (rise over run), and b is the y‑intercept (the point where the line crosses the y‑axis).

Step 2 – Compute the Slope

Select any two distinct points on the line. The slope is calculated as:

m = (Δy)/(Δx)

For example, using points (3, 4) and (5, 6):

m = (6 – 4) / (5 – 3) = 2/2 = 1

Remember that slopes can be positive or negative, so retain the sign throughout.

Step 3 – Determine the Y‑Intercept

The y‑intercept is the y‑coordinate where the line meets the y‑axis (x = 0). It can be read directly from the graph or calculated if a point with x = 0 is known. For instance, if the line crosses the y‑axis at (0, 5), then b = 5. A positive intercept indicates the line crosses above the origin, while a negative value indicates it crosses below.

Step 4 – Write the Final Equation

Substitute the computed values of m and b into the standard form:

y = mx + b

For example, with a slope of –3 and a y‑intercept of 5, the equation reads y = –3x + 5. The equation is correct when both m and b are accurately inserted, and the signs are preserved.

TL;DR

Be careful with negative signs. If b = –8 and m = 5, the equation becomes y = 5x – 8. When in doubt, double‑check your calculations.