Writing Equations of Lines
Next Lesson
Coordinate Geometry
Summary
Writing equations of lines on the ACT often starts with identifying slope and y-intercept from a graph or using given numerical information such as a slope and point or two points. Once the line’s equation is found, you can answer related questions like unknown coordinates, x-intercepts, and other point values either algebraically or graphically.
- A line’s equation can come from a graph by reading the slope and y-intercept directly, then using slope-intercept form to solve for unknown values on the line.
- When a graph shows the line and a point with an unknown coordinate, use the visual slope and y-intercept to build the equation, then substitute the point to solve the missing value.
- A slope and one point determine a unique line, so plug the slope into y = mx + b and substitute the point to solve for b before finding quantities like the x-intercept.
- Many line problems can be solved two ways: algebraically by forming and solving equations, or graphically by using slope triangles and proportional reasoning.
- Two points also determine a unique line: first compute the slope, then use either point to solve for b and write the full equation.
- Graphical reasoning remains useful after finding the slope, because partial runs and rises can be scaled proportionally to locate unknown coordinates without fully relying on algebra.
- The key strategy is to move flexibly among graphs, slopes, points, and slope-intercept form so you can choose the fastest method on test day.
Chapters
00:00
Finding a Line Equation from a Graph
01:44
Using a Slope and One Point
02:28
Finding an X-Intercept Algebraically or Graphically
09:41
Core ACT Strategies for Line Questions