Graphing Lines
Next Lesson
Coordinate Geometry
Summary
Graphing lines on the ACT begins with three core ideas: each line has a unique equation, every point on that line satisfies the equation, and every standard linear equation represents a line in the x-y plane. A line can be graphed by finding points that satisfy its equation, and this same principle also helps solve for unknown values when a point lies on a line.
- Graphing lines starts with a conceptual foundation: lines in the x-y plane are directly connected to equations, and understanding that relationship matters before focusing on graphing mechanics.
- Each line has its own unique equation, creating a one-to-one match between a line in the plane and its algebraic representation.
- Every point on a line has coordinates that satisfy the line’s equation, and this principle applies to infinitely many points on that line.
- Any ordinary equation with x and y both to the first power, without variable multiplication, division, or radicals, is a linear equation and must represent a line.
- A line can be graphed by plugging in values such as x = 0 or y = 0 to generate points, then plotting those points and drawing the line through them.
- Because any point on the line must satisfy the equation, a known point can be substituted into an equation with an unknown constant to solve for that missing value.
Chapters
00:00
Introduction to Graphing Lines
00:34
Three Foundational Ideas About Lines and Equations
02:29
Using an Equation to Find Points on a Line
03:57
Applying Point Substitution to Solve for an Unknown