Linear Equations – Writing y = mx + c from a Pattern

Every linear relationship can be captured in a single compact equation: y = mx + c, where m is the constant rate of change (how much y changes per step) and c is the starting value (the value of y when x = 0). Once you can spot a linear pattern or read a function table, writing its equation is simply a matter of identifying these two numbers.

This page focuses on writing the equation of a linear relationship from a description, pattern, or table – a distinct skill from solving a one-variable linear equation, which you covered earlier in this course. Once you're comfortable writing y = mx + c, the following pages take a much deeper dive into the parts of this equation and its variations.

Finding m and c

Real-Life Application

• Pricing formulas: writing a cost equation from a flat fee and per-unit rate.
• Growth models: writing an equation for a plant's height from its starting height and growth rate.
• Billing: writing a phone or utility bill formula from a table of past bills.

Key Takeaways

Practice: Writing Linear Equations