Respuesta :

jasonwhite3369

Answer:

y=3x-2

Step-by-step explanation:

y-y0=m(x-x0)

y-4=3x-6

y=3x-2

[tex]\rule{300}{1}\\\dashrightarrow\large\blue\textsf{\textbf{\underline{Given question:-}}}[/tex]

Find the equation of a line that passes through (2,4) and has a gradient of 3.

[tex]\dashrightarrow\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}[/tex]

First, let's take a look at our provided information.

| Provided information:-

  • Point (2,4)
  • Gradient  3

What we need to find:-

  • the line's equation

How to find it using our provided information (gradient & point)?

  •   write the equation of the line in point-slope form

point-slope form:-

  • [tex]\sf{y-y_1=m(x-x_1)}[/tex]

how to solve:-

  • Replace y₁ with 4
  • Replace m with 3 (m is the gradient)
  • Replace x₁ with 2

therefore,

  • [tex]\sf{y-4=3(x-2)}[/tex]

[tex]\bigstar[/tex] On simplification,

  • [tex]\sf{y-4=3x-6}[/tex]

[tex]\bigstar[/tex] On further simplification,

  • [tex]\sf{y=3x-6+4}[/tex]

Which results in:-

  • [tex]\sf{y=3x-2}[/tex]

Good luck with your studies.

[tex]\rule{300}{1}[/tex]

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