Equations of lines

Learning Objectives Identify the slope and y-intercept from a linear equation. Write the equation of a line in slope-intercept form (y = mx + b). Write the equation of a line in point-slope form (y - y₁ = m(x - x₁)). Convert linear equations between slope-intercept, point-slope, and standard forms. Determine the equation of a line given two points on the line. Find the equation of a line that is parallel or perpendicular to a given line and passes through a specific point. Ever wonder how your phone's GPS calculates the straightest path from your home to school? 🗺️ It's all about the math of straight lines! This tutorial will guide you through the different ways to write and understand the equations of straight lines. Mastering these forms is a foundational skill...

TermDefinitionExample Slope (m)The measure of a line's steepness and direction. It's calculated as the 'rise' (vertical change) over the 'run' (horizontal change) between any two points on the line.A line passing through (1, 2) and (3, 6) has a slope m = (6-2)/(3-1) = 4/2 = 2. For every 1 unit it moves to the right, it moves 2 units up. Y-intercept (b)The point where the line crosses the vertical y-axis. The x-coordinate of this point is always 0.If a line has a y-intercept of -5, it passes through the point (0, -5). Parallel LinesTwo or more lines in a plane that never intersect. Parallel lines always have the exact same slope.The lines y = 3x + 2 and y = 3x - 7 are parallel because both have a slope of m = 3. Perpendicular LinesTwo lines that intersect at a...

Slope-Intercept Form y = mx + b This is the most common form, where 'm' is the slope and 'b' is the y-intercept. It's extremely useful for quickly identifying a line's properties and for graphing. Point-Slope Form y - y₁ = m(x - x₁) Use this form when you know the slope 'm' and any single point (x₁, y₁) on the line. It is the most direct way to write an equation from this information. Slope Formula m = (y₂ - y₁) / (x₂ - x₁) Use this formula to calculate the slope 'm' of a line when you are given any two points (x₁, y₁) and (x₂, y₂) on that line. Standard Form Ax + By = C In this form, A, B, and C are integers, and A is usually non-negative. It's useful for finding x- and y-intercepts quickly and for worki...