#Linear vs. Exponential Growth: Your Night-Before-the-Test Guide

Hey there! Let's nail down linear and exponential growth – two concepts that are super important for the SAT Math section. Think of this as your cheat sheet for tonight. We'll make sure you're not just memorizing, but understanding how these things work. Let's get started!

#Linear Growth: Steady and Predictable

#Defining Linear Growth

• Constant Rate of Change: Linear growth means things change at the same rate. Think of it like a car going at a steady speed.
• Same Amount Each Time: For every step forward (or backward) in your 'x' value, your 'y' value changes by the same exact amount.
• Slope is Key: The slope, calculated as $$\frac{y_2 - y_1}{x_2 - x_1}$$, is that constant rate of change. It's the 'm' in our equation.
• Y-Intercept: This is where we start – the initial value when x is zero. It's the 'b' in our equation.

#Linear Function Representation

• Slope-Intercept Form: The equation $y = mx + b$ is your best friend here.

• Table Values: You'll see a constant difference in 'y' values when 'x' values change by a constant amount.

• Straight Line: The graph of a linear function is always a straight line. It can go up (positive slope), down (negative slope), or be flat (zero slope).

#Exponential Growth: Fast and Furious

#Defining Exponential Growth

• **Constant Per...