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Steepness as a Number

Part of the Graphs & Systems section of Coddy's Algebra journey. Lesson 11 of 64.

Lines differ in how fast they climb, and one number captures it: the slope, written m. Walk from any point of the line to any other: the slope is the rise (how far up) divided by the run (how far right).

m = rise/run

$From (1, 1) to (3, 5): rise 4, run 2, slope 2$

From (1, 1) to (3, 5): rise 4, run 2, slope 2

From (1, 1) to (3, 5) the rise is 4 and the run is 2, so m = 4/2 = 2: the line climbs two steps for every step right. The same answer comes from any two of its points; that constancy is what makes a line a line.

Challenge

A line passes through (2, 1) and (4, 7). Work out the rise and the run, and find its slope m.

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

All lessons in Graphs & Systems

1The Coordinate Plane

Two Numbers, One Point The Four Quadrants Points on the Axes Mirror Points Recap: The Plane

4Slope-Intercept Form

y = mx + b The Starting Height Write the Equation Solve for y Draw From Any Form Recap: y = mx + b

7Parallel & Perpendicular

Same Slope, Never Meet The Perpendicular Slope A Right-Angle Line Recap: Two Relations

10Systems by Graphing

Two Lines, One Answer Solve by Drawing Check the Crossing When Lines Never Cross Recap: By Graphing

2From Rule to Line

A Rule Makes Points The Points Line Up On the Line or Not?Between the Dots Recap: Rule to Line

5Point-Slope Form

A Point and a Slope From Two Points Flat or Vertical Through Draw From a Point Recap: Point-Slope

8Function Notation

The Name of a Rule Inputs With Signs Find the Input The Graph of f Recap: f(x)

11Solving Systems Exactly

Substitution Isolate First Elimination Scale, Then Add Three Unknowns Two Numbers, Two Facts Recap: Two Methods

3Slope

Steepness as a NumberSlope From Two Points Downhill Lines Flat and Straight Up A Fraction of a Slope Recap: Slope

6Standard Form

Ax + By = C The Two Intercepts Draw by Intercepts Between the Forms Recap: Standard Form

9Shaded Regions

A Line Splits the Plane Solid or Dashed Test a Point Rearrange, Then Shade Recap: Half-Planes

12Final Challenges

Two Shadings Overlap The Corner of a Region Final: Round Trip Final: Where They Meet Final: Draw the Fence Final: The Whole Plane

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