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The Standard form of a Linear EquationPowerPoint Presentation

The Standard form of a Linear Equation

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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
- 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 Form

- Write in standard form with
integer coefficients

- Isolate the :
- Variable terms → Left
- Constant term → Right.

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

- 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

- 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 line
- y-coordinate of 2
- Standard form is y=2.
- Vertical line
- x-coordinate of 1
- Standard form is x=1.

Practice

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

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