Standard Form and Writing Equations

Definition of a Linear Equation in Standard Form

•

An equation that can be written in the form: Ax + By = C . Where A,B, and C are real numbers.

Rules for Standard Form

• •

The lead coefficient or “A” needs to be positive, if it is negative multiply through by -1.

Standard Form does not have fractions, to remove fraction multiply each term by the least common multiple.

Example #1

Identify A, B, and C of the linear equation 3x  y  5 A= B= C= 3 1 5

Rewrite in Standard Form.

4

x

 7  2

y

4

x

 2

y

 7

Rewrite in Standard Form .

x

 12

x

 0

y

 12

Writing an Equation in Std. Form

•

To write an equation when you are given slope and y intercept, substitute the given values (m & b) into y = mx + b, then rearrange into standard form.

Write an equation for a line with a slope of 4 and a y-intercept of 2, in standard form.

y



mx



b



y

 4

x

4

x



y

  2 2

Std

.

Form Ax



By



C

4

x



y

  2

Write an equation for a line in standard form.

y

2   2 2

x

5 

x

5 5 

y x y

   3 3 15

Std

.

Form Ax



By



C

Write an equation for a line, in standard form.

Given :

m

  3 4

y

0   3

y

  3 3 3 4

x



x

 4

y

4

y



x

   3 3  12

Standard Form and Writing Equations Algebra 1