Question

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

Answer 1

y=3x-2

Explanation:

y-y0=m(x-x0)

y-4=3x-6

y=3x-2

Answer 2

`\rule{300}{1}\\\dashrightarrow\large\blue\textsf{\textbf{\underline{Given question:-}}}`

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

`\dashrightarrow\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}`

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:-

• 
  `\sf{y-y_1=m(x-x_1)}`

how to solve:-

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

therefore,

• 
  `\sf{y-4=3(x-2)}`

`\bigstar` On simplification,

• 
  `\sf{y-4=3x-6}`

`\bigstar` On further simplification,

• 
  `\sf{y=3x-6+4}`

Which results in:-

• 
  `\sf{y=3x-2}`

Good luck with your studies.

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