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12. Write an equation in standard form of a line whose intercepts are fractions.
Explain how you know the intercepts are fractions.

Respuesta :

calculista

Answer:

see the explanation in the procedure

Step-by-step explanation:

we know that

The equation of a line in standard form is

[tex]Ax+By=C[/tex]

where

A is a positive integer

B and C are integers

Find the intercepts

Find the y-intercept

The y-intercept is the value of y when the value of x is equal to zero

so

For x=0

[tex]By=C[/tex]

[tex]y=\frac{C}{B}[/tex]

In order for C/B to be a fraction, C must not be a multiple of B

Find the x-intercept

The x-intercept is the value of x when the value of y is equal to zero

so

For y=0

[tex]Ax=C[/tex]

[tex]x=\frac{C}{A}[/tex]

In order for C/A to be a fraction, C must not be a multiple of A

adioabiola

The y- and x- intercepts of a line take fractional forms C/B and C/A respectively. However, for the intercepts to be fractions; C must not be a multiple of neither A nor B.

The equation of a line in standard form usually takes the form;

  • Ax + By = c

where A , B and C are arbitrary constants.

Therefore,

For y-intercept:

  • We must set, x = 0.
  • By = C
  • y = C/B

The y-intercept as a fraction is therefore, y = C/B

  • where C must not be a multiple of B

For x-intercept;

  • We must set, y = 0.
  • Ax = C
  • x = C/A

The x-intercept as a fraction is therefore, y = C/A

where C must not be a multiple of A.

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