Question

What is the equation of the line that is parallel to \[y=-4\] and passes through the point \[(3,7)\]?
(A) \[y=3x-4\]
(B) \[y=3\]
(C) \[y=3x+7\]
(D) \[y=7\]

Answer 1

Hint: In the above question, we have to find the equation of the line which is parallel to a given line, and the points are also given through which the line passes. So before solving this question, we should know that the two lines which are parallel to each other in a plane will have the same slope.

Complete step by step answer:
A straight line is a two-dimensional figure in which the slope of the line measures the steepness of the line. We can find the slope of the line using different forms of equations.
The first one is slope point form which is given as shown below.
\[y-{{y}_{1}}=m(x-{{x}_{1}})\]
Where the slope m is given by \[m=\tan \theta \], where \[\theta \] is the angle formed by the line with the positive x-axis, and the line passes through the point \[({{x}_{1}},{{y}_{1}})\].
The second one is the two-point form which is given as shown below.
\[y-{{y}_{1}}=\left( \dfrac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}} \right)(x-{{x}_{1}})\]
Where the given line passes through the point \[({{x}_{1}},{{y}_{1}})\] and \[({{x}_{2}},{{y}_{2}})\].
The third one is the intercept form which is given as shown below.
\[\dfrac{x}{a}+\dfrac{y}{b}=1\]
Where a represents the x-intercept at the x-axis and b represents the y-intercept on the y-axis.
In the above question, we have to find the equation of the line which is parallel to the given line \[y=-4\] and passes through the point \[(3,7)\].
The standard equation of the line is given as shown below.
\[y=mx+c\]…….eq(1)
Where x and y are the points that touch the line, m is the slope of the line and c is the constant.
On comparing the line \[y=-4\] to eq(1)
\[y=0\times x-4\]
So the slope of the line will be zero because this line is parallel to the line which we will obtain.
So the line that passes through the point \[(3,7)\] and having slope zero will be written as.
\[\begin{align}
  & y=mx+c \\
 & \Rightarrow 7=0\times 3+c \\
 & \Rightarrow c=7 \\
\end{align}\]
So after putting these value is eq(1), we will get the equation which is parallel to \[y=-4\] and passes through the point \[(3,7)\]
\[\begin{align}
  & y=0\times x+7 \\
 & \Rightarrow y=7 \\
\end{align}\]

So, the correct answer is “Option D”.

Note:
A straight line has an infinite length and we can never calculate the distance between two extreme points. A straight line does not have any area or volume. A straight line is known as a one-dimensional figure and an infinite number of lines can pass through a given point but only one line can pass through two given points.