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Module 8: Linear Equations and Linear Systems

Formulating Linear Equations

When at least two points are given, we can determine a linear equation in slope-intercept form corresponding to those points. The key is to obtain the slope and y-intercept.

Tutorial 33: How to Determine the Slope-Intercept Linear Equation of a Line given Two Points

Example:

(1,0) and (2,4)

  1. Determine the slope between the two given points. Use the rise over run formula. Consider the second coordinate to be the one further along the x axis.

    r i s e r u n = y 2 − y 1 x 2 − x 1 {"version":"1.1","math":"\dfrac{rise}{run}= \dfrac{y_2-y_1}{x_2-x_1} "}

    m = 4 − 0 2 − 1 {"version":"1.1","math":"m= \dfrac{4-0}{2-1} "}

    m = 4 1 → 4 {"version":"1.1","math":"m= \dfrac{4}{1} \rightarrow4"}

  2. Now it’s time to find the y-intercept (b). To do so, plug m and x/y from one of the two given points into the general slope-intercept form. Isolate and solve for b.

    y = m x + b {"version":"1.1","math":"y=mx+b "}

    ( 0 ) = ( 4 ) ( 1 ) + b {"version":"1.1","math":"(0)=(4)(1)+b "}

    0 = 4 + b {"version":"1.1","math":"0=4+b "}

    0 − 4 = b {"version":"1.1","math":"0−4=b "}

    − 4 = b {"version":"1.1","math":"−4=b "}

  3. Form the equation using m {"version":"1.1","math":"m"} and b {"version":"1.1","math":"b"}.

    y = 4 x − 4 {"version":"1.1","math":"y=4x−4 "}

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