Slope and Y-Intercept

Slope measures how steep a line is — it tells you how much y changes for every 1 unit increase in x. [formula] Types of slope: - Positive slope (m > 0): line goes up from left to right ↗ - Negative slope (m < 0): line goes down from left to right ↘ - Zero slope (m = 0): horizontal line → - Undefined slope: vertical line ↑ (division by zero)

Example: Find the slope of the line through (1, 3) and (4, 9).

The y-intercept is the point where the line crosses the y-axis. At this point, x = 0. We write it as the point (0, b) or just the value b. To find the y-intercept from an equation: set x = 0 and solve for y. To find it from a graph: look where the line crosses the y-axis.

Example: Find the y-intercept of y = 3x + 7.

On the SAT, slope and y-intercept often represent real-world quantities: - Slope = rate of change (cost per item, speed, growth rate) - Y-intercept = starting value (initial cost, initial amount, base fee) Example: In C = 15t + 50, where C is total cost and t is hours: - Slope = 15 → the cost increases by 15$ per hour - Y-intercept = 50 → there's a 50 base fee (the cost when t = 0$)

Example: A pool is being filled. The depth (in inches) after t minutes is modeled by d = 0.5t + 4. What do the slope and y-intercept represent?

Slope questions appear on every SAT. The fastest way to find slope from a graph: pick two points where the line clearly crosses grid intersections, then count the rise and run. For interpretation questions, always translate slope as 'the change in y for each 1-unit increase in x'.