The standard form of a linear equation
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The Standard form of a Linear Equation. BY. Juran & Viki. Writing an Equation in Standard Form. Most are written in slope-intercept form. Slope-intercept form : y=mx+b Another used form : → standard form Standard(or general) form : Ax+By=C

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The Standard form of a Linear Equation

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The standard form of a linear equation

The Standard form of a Linear Equation

BY. Juran & Viki


Writing an equation in standard form

Writing an Equation in Standard Form

  • Most are written in slope-intercept form.

  • Slope-intercept form : y=mx+b

  • Another used form :

    →standard form

  • Standard(or general) form : Ax+By=C

  • Variable terms:on Left side / Constant term : Right side

    A, B, C represent real numbers

    A and B are not both 0.


Writing an equation in standard form1

Writing an Equation in Standard Form

  • Write in standard form with

    integer coefficients

  • Isolate the :

    • Variable terms → Left

    • Constant term → Right.


Solution

Solution

  • Write original Equation

  • Multiply each side by 5

  • 5y=2x-15 Use distributive property

  • -2x+5y=-15 Subtract 2x from each side


Standard form

Standard Form

  • A linear equation can have more than one standard form.

  • EX.) If you multiply each side of the standard form above by -1, you get

    2x-5y=15

Standard Form


Writing linear equations

Writing Linear Equations

  • Standard form of a line passing through (-8,6) with a slope of -2.

  • y-y₁=m(x-x₁) -> Write point-slope form.

  • y-6=-2(x+8) -> Substitute.

  • y-6=-2x-16 -> Distributive property.

  • 2x+y=-10 -> Add 2x and 6.

  • Finished!!!


Horizontal and vertical lines

Horizontal and Vertical Lines

  • Horizontal line

  • y-coordinate of 2

  • Standard form is y=2.

  • Vertical line

  • x-coordinate of 1

  • Standard form is x=1.


Practice

Practice

  • Standard form, standard form, standard form…

  • (1,4) m=2(0, 356)

  • y-2x=2y=356

  • x+3y-4=0

  • x+3y=4


The standard form of a linear equation

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