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Module 8: Linear Equations and Linear Systems

Slope/Intercept

The slope ( m {"version":"1.1","math":"m"}) defines the steepness of the incline of a linear equation when graphed out.

  • Can be described as “rise over run”.
  • For consistency, consider a line as it we move from left to right.
  • The numerator of m is the rise of the incline (when negative, it goes downward).
  • The denominator of m is the run of the incline (rightward movement.
  • For example: m = − 2 3 {"version":"1.1","math":"m=-\dfrac{2}{3}"}, getting from one point to another requires a vertical descent of 2 down and horizontal run of 3 to the right.

Tutorial 36: How to Graph Using Slope and Y-intercept

Example:

y = 2 x + 1 {"version":"1.1","math":"y=2x+1 "}

 

  1. Determine the slope (m) and y-intercept from the equation (b).

    y-intercept

    b = 1 {"version":"1.1","math":"b=1"}

    y − i n t : 0.1 {"version":"1.1","math":"y−int:0.1 "}

    slope

    m = 2 1 {"version":"1.1","math":"m=\dfrac{2}{1}"}

    → r i s e o f 2 , r u n o f 1 {"version":"1.1","math":"\rightarrow\;rise\;of\;2,\;run\;of\;1"}

    → + 2 t o y , + 1 t o x {"version":"1.1","math":"\rightarrow\;+2\;to\;y,\;+1\;to\;x"}

  2. Locate the next coordinate point over to the right from the y-intercept using the slope and plot both on the Cartesian plane.

    0 , 1 → 0 + 1 , 1 + 2 → ( 1 , 3 ) {"version":"1.1","math":"0,1→0+1, \;1+2→(1,3) "}

  3. Connect the dots and extend the line.

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