# The Standard form of a Linear Equation - PowerPoint PPT Presentation

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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

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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