Key Concepts

Key Concepts

• Find the Slope of a Line from its Graph using \(m=\frac{\text{rise}}{\text{run}}\)
  
  1. Locate two points on the line whose coordinates are integers.
  2. Starting with the point on the left, sketch a right triangle, going from the first point to the second point.
  3. Count the rise and the run on the legs of the triangle.
  4. Take the ratio of rise to run to find the slope.
• Graph a Line Given a Point and the Slope
  
  1. Plot the given point.
  2. Use the slope formula \(m=\frac{\text{rise}}{\text{run}}\) to identify the rise and the run.
  3. Starting at the given point, count out the rise and run to mark the second point.
  4. Connect the points with a line.
• Slope of a Horizontal Line
  
  • The slope of a horizontal line, \(y=b\), is 0.
• Slope of a vertical line
  
  • The slope of a vertical line, \(x=a\), is undefined

Glossary

geoboard

A geoboard is a board with a grid of pegs on it.

negative slope

A negative slope of a line goes down as you read from left to right.

positive slope

A positive slope of a line goes up as you read from left to right.

rise

The rise of a line is its vertical change.

run

The run of a line is its horizontal change.

slope formula

The slope of the line between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2−y_1}{x_2−x_1}$.

slope of a line

The slope of a line is $m=\frac{\text{rise}}{\text{run}}$. The rise measures the vertical change and the run measures the horizontal change.