Answer

Verified

391.2k+ views

**Hint:**In order to find a solution to this problem, we will first have to analyze points that is $x$ and $y$coordinate from the given point and substitute in point-slope formula that is, $\left( y-{{y}_{1}} \right)=m\left( x-{{x}_{1}} \right)$.

**Complete step-by-step solution:**

We will start the solution by considering the given point as point $P\left( 4,2 \right)$.

Now we have our point $P$ that has two coordinates $x$ and $y$, so we have ${{x}_{1}}=4$ and ${{y}_{1}}=2$.

Now also we have our slope that is given in our problem that is $m=-2$.

Therefore, with this, we have all our requirements to write an equation in standard format.

We know standard form of equation as, $y=mx+c$ (where $m$ is the slope and $\left( x,y \right)$ is a point the line that passes through)

Hence, now we will substitute in the point-slope formula that is, $\left( y-{{y}_{1}} \right)=m\left( x-{{x}_{1}} \right)$.

So by substituting values, we get:

$\left( y-2 \right)=-2\left( x-4 \right)$

Now evaluating and simplifying above equation, we get:

$y-2=-2x+8$

Now transferring values from right hand side to left hand side and simplifying, we get:

$2x+y-2-8=0$

$2x+y-10=0$

Now by simplifying the equation into standard form that is, $y=mx+c$ we get:

$y=-2x+10$

Therefore, $y=-2x+10$ is the standard form of the equation of line.

We can represent this equation of line in graph form as:

**Note:**The equation of a line can be found through various methods, some of the methods are Point-slope form, Slope-intercept form, Intercept form, Two-point form and depending on the available information we can write the equation of line.

After finding out the equation of line from one of the above methods, we have to write in a standard form that is, $y=mx+c$ , where $m$ is the slope and $\left( x,y \right)$ is a point that passes through the line.

Recently Updated Pages

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Advantages and disadvantages of science

10 examples of friction in our daily life

Trending doubts

Which are the Top 10 Largest Countries of the World?

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Who was the first to raise the slogan Inquilab Zindabad class 8 social science CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

One cusec is equal to how many liters class 8 maths CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

A resolution declaring Purna Swaraj was passed in the class 8 social science CBSE