Coordinate Plane - GED Math - Inequalities and Slope

Q: How do you graph one-variable inequalities on a number line?

Isolate the variable to determine the arrow direction. Use an open circle for “greater than” and “less than,” and a closed circle for “greater than or equal to” and “less than or equal to.”

Q: What does an ordered pair (x, y) mean on the coordinate plane?

The first number is the distance from the origin along the x-axis, and the second number is the distance from the origin along the y-axis.

Q: How is slope calculated for a line on the coordinate plane?

Slope is measured by dividing the difference in y-coordinates by the difference in x-coordinates, described as “rise over run.”

Sep 14, 2026

Uploaded by Callum

Coordinate Plane lesson content focuses on graphing linear equations, linear inequalities, and interpreting graphs and functions. It explains how to use number lines for one-variable inequalities, including open versus closed circles for strict and inclusive comparisons. The lesson then builds coordinate-plane skills by using ordered pairs, the origin, and points’ x/y distances. It concludes with slope concepts, including the rise-over-run method and how slope types (positive, negative, zero, undefined/vertical) describe line direction.

LanguageEnglish

CategoryExam

FormatPDF

Pages58

Reading Time2 h 26 min

AccessFree to download

Learning Objectives

Graphing One-Variable Inequalities

Open and closed circles for inequality symbols

Graphing on the Coordinate Plane

Ordered pairs and origin

Mixed Practice

Slope

Rise over run and slope types

The Coordinate Plane Learning Objectives By the end of this lesson, you will be able to: • Graph linear equations • Graph linear inequalities • Connect and interpret graphs and functions • Connect coordinates, lines, and equations Graphing One-Variable Inequalities An inequality with only one variable is graphed on a number line. Isolate the variable to determine the direction of the arrow. Use an open circle to denote: • “greater than”(>) • “less than”(<) Use a closed circle to denote: • “greater than or equal to”(≥) • “less than or equal to”(≤) x 􀀡􀀐3 x 􀀟 2 x 􀁴􀀐2 x 􀁤 1 Mixed Practice 1. Julia wants to spend $100 or less ordering shirts from an online company. The company charges a $5 shipping fee for any order. The inequality 5 + 15n < 100 represents the number of shirts, n, Julia can order from the online company. Graph all possible numbers of shirts Julia can buy. Click on the number line to plot the point(s) . 1 2 3 4 5 6 7 8 9 10 Graphing on the Coordinate Plane A coordinate plane is formed by two intersecting lines: an x-axis and ay-axis. The x-axis is horizontal and the y-axis is vertical. The point at which the x-axis andy-axis meet is called the origin. Graphing on the Coordinate Plane Each point in the coordinate plane can be named using an ordered pair. The first number is the distance from the origin along the x-axis. The second number is the distance from the origin along the y-axis. The point P is at (–1,–3) and the point M is at (2, 3) . Mixed Practice 2. What is the ordered pair for Point H? A. (7,–2) B. (7, 2) C. (–2, 7) D. (–2,–7) Slope A linear equation has two variables and is graphed on a coordinate plane using a line. The slope of the line is measured by dividing the difference in y-coordinates by the difference in x-coordinates, or finding the “rise over run.” The slope formula can be found on the GED Formula Sheet, but you should plan on memorizing it: m 􀀠 y2 􀀐 y1 x 2 􀀐 x1 The slope of the line with points (2, 2) and (1,–1) is: 􀀐1􀀐 2 􀀐3 m 􀀠 􀀠 􀀠 3 1􀀐 2 􀀐1 Mixed Practice 3. A telemarketing company tracks employee efficiency. Use the graph to find the rate of calls made per hour of work. A. 0.055 calls per hour B. 17.25 calls per hour C. 18.25 calls per hour D. 69 calls per hour Slope A line with a positive slope runs “uphill,” and a line with a negative slope runs “downhill.” A line with a slope of zero is “flat,” and a line with an undefined slope is vertical, like a cliff. Line n has a positive slope. Line l has a negative slope. Line k has a slope of zero. Line m has an undefined slope.

FAQs

How do you graph one-variable inequalities on a number line?

Isolate the variable to determine the arrow direction. Use an open circle for “greater than” and “less than,” and a closed circle for “greater than or equal to” and “less than or equal to.”

What does an ordered pair (x, y) mean on the coordinate plane?

The first number is the distance from the origin along the x-axis, and the second number is the distance from the origin along the y-axis.

How is slope calculated for a line on the coordinate plane?

Slope is measured by dividing the difference in y-coordinates by the difference in x-coordinates, described as “rise over run.”

Sep 14, 2026

Uploaded by Callum