Intercept and Slopes

When looking at graphs, intercepts are where lines cross the axes. An x-intercept is where the line crosses the x-axis (with y always equal to 0), while a y-intercept is where it crosses the y-axis (with x always equal to 0). Finding them is simple: for x-intercepts, set y=0 and solve; for y-intercepts, set x=0 and solve.

Slope measures how steep a line is—it tells you how much the y-value changes when x increases by 1. The formula is m = $y₂-y₁$/$x₂-x₁$ using two points on the line. In the equation y = mx + b, m represents the slope. Positive slopes go upward, negative slopes go downward, and zero slopes are flat horizontal lines. Vertical lines have undefined slopes (since you'd divide by zero).

Lines can relate to each other through their slopes too. Parallel lines have the same slope—they never meet no matter how far they extend. Perpendicular lines have slopes that are negative reciprocals of each other $their slopes multiply to give -1$, and they meet at perfect right angles.

Pro Tip: When you're stuck on a line problem, remember that the slope is like the line's personality—it tells you everything about how the line behaves. A slope of 2 means "up 2, right 1" while a slope of -3 means "down 3, right 1."