Answer
Verified
412.2k+ views
Hint: Here, the points are given with its slope and we have to make the equation.
For that we have to first use the point-slope formula as the points and slope are given.
The formula for points slope is
$\left( y-{{y}_{1}} \right)=m\left( x-{{x}_{1}} \right)$
Where, $m=$ slope of the line
$\left( {{x}_{1}},{{y}_{1}} \right)=$ Points given in the numerical from this formula we can calculate the equation. After simplifying the equation, compare that equation with standard slope intercept formula i.e.
$y=mx+b$
Where, $m=$ slope of the line
$b=$ $y$-intercept.
Complete step by step solution:
Given that, there is point $P\left( 8,2 \right)$ from which a line is passing whose slope is $4.$
We know the formula of point slope, from that we can find out the equation.
So, the formula for point-slope formula is,
$\left( y-{{y}_{1}} \right)=m\left( x-{{x}_{1}} \right)...(i)$
Where, $m$ is slope is given in the numerical i.e. $4$ and $\left( {{x}_{1}},{{y}_{1}} \right)$ are the points from which the line is passing i.e. $\left( 8,2 \right)$
From above we can say that,
$m=4$
${{x}_{1}}=8$
${{y}_{1}}=2$
Put this value in equation $(i)$ we get,
$\left( y-2 \right)=4\left( x-8 \right)...(ii)$
We have to convert the above equation in the form of slope-intercept equation.
The formula of the slope-intercept for the linear equation is as,
$y=mx+b...(iii)$
Now, simplify the equation $(ii)$
$\left( y-2 \right)=4\left( x-8 \right)$
Multiply whole bracket with $4$ on right side
$y-2=4\times x-4\times 8$
$\Rightarrow y-2=4x-32$
Transpose $2$ on the right side of the equation,
$y=4x-32+2$
$\Rightarrow y=4x-30...(iv)$
Now compare equation $(iii)$ and $(iv)$
$y=mx+b$
$\Rightarrow y=4x-30$
From above, the value of $m=4$ and $b=-30$
Therefore the equation for the given point $P\left( 8,-2 \right)$ is $y=4x-30$
Additional Information:
The formula for slope intercept for a linear equation is given as,
$y=mx+b$
Where, $m=$slope of the line
$b=y$-intercept
The slope $(m)$ in above formula is nothing but eh change in $y$ to the change in $x$
It is generally called as ratio of rise to run i.e. $\dfrac{rise}{run}$
It can also be written as $\dfrac{\Delta y}{\Delta x}$. When we have two point on the line $9.$ $\left( {{x}_{1}},{{y}_{1}} \right)\And \left( {{x}_{2}},{{y}_{2}} \right)$ then we can use following formula for calculating slope $(m)$
The formula of slope for $2$ points.
$m=\dfrac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}$
The $y$-intercept is nothing but the value where the $y$-axis is touched or intersects by the line.
Note: In this numerical the two equations are used. Both the equations are related to the slope-intercept equation.
The first formula used is slope-points which is used for nothing but calculating the slope $(m)$ But the value of $m$ is already given. So we have to calculate the value of $b$ for the slope intercept. Formula which is the second equation.
And we have to simplify that equation into slope intercept form.
We use the point-slope equation formula for getting the equation in the term of slope intercept which is the standard equation.
For that we have to first use the point-slope formula as the points and slope are given.
The formula for points slope is
$\left( y-{{y}_{1}} \right)=m\left( x-{{x}_{1}} \right)$
Where, $m=$ slope of the line
$\left( {{x}_{1}},{{y}_{1}} \right)=$ Points given in the numerical from this formula we can calculate the equation. After simplifying the equation, compare that equation with standard slope intercept formula i.e.
$y=mx+b$
Where, $m=$ slope of the line
$b=$ $y$-intercept.
Complete step by step solution:
Given that, there is point $P\left( 8,2 \right)$ from which a line is passing whose slope is $4.$
We know the formula of point slope, from that we can find out the equation.
So, the formula for point-slope formula is,
$\left( y-{{y}_{1}} \right)=m\left( x-{{x}_{1}} \right)...(i)$
Where, $m$ is slope is given in the numerical i.e. $4$ and $\left( {{x}_{1}},{{y}_{1}} \right)$ are the points from which the line is passing i.e. $\left( 8,2 \right)$
From above we can say that,
$m=4$
${{x}_{1}}=8$
${{y}_{1}}=2$
Put this value in equation $(i)$ we get,
$\left( y-2 \right)=4\left( x-8 \right)...(ii)$
We have to convert the above equation in the form of slope-intercept equation.
The formula of the slope-intercept for the linear equation is as,
$y=mx+b...(iii)$
Now, simplify the equation $(ii)$
$\left( y-2 \right)=4\left( x-8 \right)$
Multiply whole bracket with $4$ on right side
$y-2=4\times x-4\times 8$
$\Rightarrow y-2=4x-32$
Transpose $2$ on the right side of the equation,
$y=4x-32+2$
$\Rightarrow y=4x-30...(iv)$
Now compare equation $(iii)$ and $(iv)$
$y=mx+b$
$\Rightarrow y=4x-30$
From above, the value of $m=4$ and $b=-30$
Therefore the equation for the given point $P\left( 8,-2 \right)$ is $y=4x-30$
Additional Information:
The formula for slope intercept for a linear equation is given as,
$y=mx+b$
Where, $m=$slope of the line
$b=y$-intercept
The slope $(m)$ in above formula is nothing but eh change in $y$ to the change in $x$
It is generally called as ratio of rise to run i.e. $\dfrac{rise}{run}$
It can also be written as $\dfrac{\Delta y}{\Delta x}$. When we have two point on the line $9.$ $\left( {{x}_{1}},{{y}_{1}} \right)\And \left( {{x}_{2}},{{y}_{2}} \right)$ then we can use following formula for calculating slope $(m)$
The formula of slope for $2$ points.
$m=\dfrac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}$
The $y$-intercept is nothing but the value where the $y$-axis is touched or intersects by the line.
Note: In this numerical the two equations are used. Both the equations are related to the slope-intercept equation.
The first formula used is slope-points which is used for nothing but calculating the slope $(m)$ But the value of $m$ is already given. So we have to calculate the value of $b$ for the slope intercept. Formula which is the second equation.
And we have to simplify that equation into slope intercept form.
We use the point-slope equation formula for getting the equation in the term of slope intercept which is the standard equation.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
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
Trending doubts
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
In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE
Which are the Top 10 Largest Countries of the World?
How do you graph the function fx 4x class 9 maths CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Why is there a time difference of about 5 hours between class 10 social science CBSE