Interactive Slope Investigation: Finding Δy and Δx

Help students build a deep, conceptual understanding of slope, linear functions, and rise and run with this highly interactive worksheet. Students explore three different lines—one with slope 1, one with slope 2.5, and one with a negative slope of –1.5. For each line, they run multiple experiments, for each experiment, they are given two points and use intuitive sliders to match the horizontal distance (Δx) and vertical distance (Δy). Once they record these values, students calculate the slope and compare how different slopes affect a line’s steepness and direction on the coordinate plane.

This activity transforms slope from a memorized formula into a visual discovery process. By measuring, adjusting, and analyzing multiple examples, students see that the slope of a straight line is constant no matter which two points they choose. The worksheet also helps them distinguish between positive and negative slopes and understand how larger slopes create steeper lines.

Key Skills Students Will Develop

• Understanding rise (Δy) and run (Δx) using interactive graph tools
• Calculating slope using the formula Δy ÷ Δx
• Identifying positive, negative, and steep slopes
• Comparing slopes of multiple linear functions
• Interpreting linear relationships on the coordinate plane
• Recognizing that slope is constant across all points of a straight line
• Connecting visual right triangles to the concept of slope

What’s Included in the Worksheet

• Three linear graphs with different slopes
• Automatically selected first experiment for each line
• Two interactive sliders to model rise and run
• Table for recording Δx, Δy, and computed slope
• Multiple-choice questions to check understanding
• Clear instructions and student-friendly guidance

Perfect For

• 8th grade math
• Algebra 1 readiness
• Understanding slope from two points
• Visual and hands-on learners
• Classwork, practice, independent learning, and intervention
• Digital classrooms and remote learning platforms

Fully aligned with CCSS 8.EE.B.6, this worksheet gives students a powerful, intuitive foundation for working with linear functions and analyzing graphs—making it an excellent addition to your slope and linear relationships unit.