contestada

Write the equation of the line whose slope and the point through which it passes are given. Express the equation in standard form.
(4, -1) and slope m = 6

Respuesta :

msm555

Answer:

[tex]6x - y = 25[/tex]

Step-by-step explanation:

The equation of a line in point-slope form is given by:

[tex]\Large\boxed{\boxed{ y - y_1 = m(x - x_1)}} [/tex]

where

  • [tex](x_1, y_1)[/tex] is a point on the line, and
  • [tex]m[/tex] is the slope.

Given the point [tex](4, -1)[/tex] and the slope [tex]m = 6[/tex], substitute these values into the point-slope form:

[tex] y - (-1) = 6(x - 4) [/tex]

Simplify the equation:

[tex] y + 1 = 6x - 24 [/tex]

Subtract 1 from both sides:

[tex] y = 6x - 25 [/tex]

Now, rearrange it into standard form (where coefficients are integers and [tex]Ax + By = C[/tex]):

[tex] 6x - y = 25 [/tex]

So, the equation of the line in standard form is:

[tex]\Large \boxed{\boxed{6x - y = 25}}[/tex]

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