Question

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

Answer 1

Answer:

y=3x-2

Step-by-step 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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