A Fraction of a Slope

Part of the Graphs & Systems section of Coddy's Algebra journey. Lesson 15 of 64.

A slope need not be whole. Through (0, -1) and (6, 3) the formula gives

m = (3 - (-1))/(6 - 0) = 4/6 = 2/3

and the answer is left as the reduced fraction 2/3, never rounded to a decimal: two up for every three right is exact. A slope of 2/3 climbs gently; 3/2 climbs the same picture with the axes swapped, noticeably steeper.

Reducing matters because slopes are compared: 4/6, 6/9 and 2/3 are one slope wearing three coats. The reduced form is the one to give.

Challenge

Find the slope m of the line through (1, 1) and (5, 4), as a reduced fraction.

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 Number Slope From Two Points Downhill Lines Flat and Straight UpA Fraction of a SlopeRecap: 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