Week 1, Session 1: GED® Geometry Orientation, Formula Sheet, Units, and Calculator Readiness
Week 1, Session 2: Perimeter of Polygons and Real-World Boundary Problems
Week 2, Session 1: Area of Rectangles, Triangles, and Parallelograms
Week 2, Session 2: Polygons, Trapezoids, and Missing Dimensions
Week 3, Session 1: Circles—Radius, Diameter, Circumference, and Area
Week 3, Session 2: Composite 2-D Figures and Shaded Regions
Week 4, Session 1: Unit Conversions, Scale Drawings, Maps, and Blueprints
Week 4, Session 2: Similar Figures and Proportional Geometry
Week 5, Session 1: Pythagorean Theorem Foundations
Week 5, Session 2: Pythagorean Applications and Distance on a Grid
Week 6, Session 1: Volume of Rectangular Prisms and Triangular Prisms
Week 6, Session 2: Volume of Cylinders, Cones, Pyramids, and Spheres
Week 7, Session 1: Surface Area of Prisms and Cylinders
Week 7, Session 2: Surface Area of Pyramids, Cones, Spheres, and Nets
Week 8, Session 1: Composite 3-D Solids and Real-World Design Problems
Week 8, Session 2: Coordinate Plane Foundations—Points, Quadrants, and Distances
Week 9, Session 1: Slope from Graphs, Points, Tables, and Contexts
Week 9, Session 2: Parallel and Perpendicular Lines
Week 10, Session 1: Linear Equations and Graphing in Geometry Contexts
Week 10, Session 2: Coordinate Geometry—Area, Perimeter, and Diagonal Distance on the Grid
Week 11, Session 1: Working Backward with Geometry Formulas
Week 11, Session 2: Multi-Step GED® Geometry Word Problems and Formula Selection
Week 12, Session 1: Timed Mixed GED® Geometry Practice and Error Analysis
Week 12, Session 2: Final GED® Geometry Review and Test-Day Strategy

Free trial session

Week 9, Session 1: Slope from Graphs, Points, Tables, and Contexts

GED® Advanced Geometry: Measurement, Coordinate Geometry, and Test-Day Problem Solving · preview lesson

Week 9, Session 1: Slope from Graphs, Points, Tables, and Contexts

Self-study purpose

Slope measures steepness and rate of change. On GED® questions, slope can appear in graphs, tables, coordinate pairs, equations, and word problems.

What you should be able to do after this session

Calculate slope as rise over run.
Find slope from two points.
Find slope from a table.
Interpret positive, negative, zero, and undefined slope.

Visual model

Geometry diagram: Slope is rise over run

Formula and idea bank

Slope: \(m=\frac{\text{rise}}{\text{run}}\).
From points: \(m=\frac{y_2-y_1}{x_2-x_1}\).
Horizontal line: slope \(0\).
Vertical line: undefined slope.

Teacher explanation

Slope is a ratio of vertical change to horizontal change.
Positive slope rises left to right; negative slope falls left to right.
In context, slope often means a unit rate, such as dollars per hour or miles per gallon.

Worked example

Find the slope through \((1,3)\) and \((5,11)\): \(m=\frac{11-3}{5-1}=\frac{8}{4}=2\).

GED® problem-solving routine

Choose two points.
Subtract y-values for rise.
Subtract x-values in the same order for run.
Simplify the fraction and interpret the sign.

Common mistakes to avoid

Subtracting x-values on top.
Changing point order between numerator and denominator.
Calling vertical slope zero.

Mastery check

Before moving to the next session, complete the 10 questions below without notes. Then correct every missed problem by writing: given information → formula → substitution → answer with units.

Quick Check

What is the slope formula from two points?

Advanced Extension and Harder GED® Practice

Deeper idea

Slope measures steepness as a rate of change: \(\frac{\text{change in }y}{\text{change in }x}\). It can be read from a graph, table, two points, or word context. Positive slope rises left to right; negative slope falls left to right.

Worked example: slope from two points

Find the slope through \((-2,5)\) and \((4,-7)\).

Change in \(y\): \(-7-5=-12\).
Change in \(x\): \(4-(-2)=6\).
Slope: \(\frac{-12}{6}=-2\).

Harder GED® challenge

A water tank loses 18 gallons every 3 minutes. Let \(x\) be minutes and \(y\) be gallons. The slope is \(-18/3=-6\), meaning the amount of water decreases by 6 gallons per minute.

Advanced trap to watch

Keep the same point order in the numerator and denominator. If you start with the second point in \(y_2-y_1\), use the second point first in \(x_2-x_1\) too.