Respuesta :

jacob193

Answer:

[tex]x + y = 1[/tex].

Step-by-step explanation:

In general, [tex]A \,x + B\, y = C[/tex] is the standard form of a line. Note that [tex]A[/tex], [tex]B[/tex], and [tex]C[/tex] are constants that can be equal to zero.

The question provided the slope and the y-intercept of the line in question. Hence, start with the slope-intercept form and rewrite to produce the standard form.

The slope-intercept form of a line is in the form

[tex]y = m \, x + b[/tex],

where

  • [tex]m[/tex] is the slope of the line, and
  • [tex]b[/tex] is the y-intercept of the line (not the x-intercept.)

In this case,

  • [tex]m = -1[/tex], and
  • [tex]b = 1[/tex].

Hence the line in the slope-intercept form:

[tex]y = (-1) \, x +1[/tex], or, simply, [tex]y = -x + 1[/tex].

Rearrange the equation to produce the standard form. Add [tex]x[/tex] to both sides of the equation:

[tex]x + y = x - x + 1[/tex].

[tex]x + y = 1[/tex].

And that's the standard form of this line. In this case, [tex]\text{$A$, $B$, and $C$}[/tex] are all equal to [tex]1[/tex].

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