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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. 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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  1. The Standard form of a Linear Equation BY. Juran & Viki

  2. 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.

  3. Writing an Equation in Standard Form • Write in standard form with integer coefficients • Isolate the : • Variable terms → Left • Constant term → Right.

  4. Solution • Write original Equation • Multiply each side by 5 • 5y=2x-15 Use distributive property • -2x+5y=-15 Subtract 2x from each side

  5. 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

  6. 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!!!

  7. 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.

  8. Practice • Standard form, standard form, standard form… • (1,4) m=2 (0, 356) • y-2x=2 y=356 • x+3y-4=0 • x+3y=4

  9. THANK YOU FOR WATCHING!

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