Find the equation of line parallel to $y$ -axis and drawn through the point of intersection of the line $x - 7y + 5 = 0$ and $3x + y = 0$ .

Given, equation of lines are $x -7 y + 5 = 0\quad ...(i)$ and $3x + y = 0 \quad ...(ii)$ On solving $(i)$ and $(ii)$ , we get, $x=\frac{-5}{22}, y=\frac{15}{22}$ Hence, the intersection point is $\left(-\frac{5}{22}, \frac{15}{22}\right)$ . $\therefore$ Equation of required line is $y-\frac{15}{22}=\frac{1}{0}\left(x+\frac{5}{22}\right)$ $\Rightarrow 0=x+\frac{5}{22}$ $(\because$ Line is parallel to $y$ -axis $\therefore m=tan\,90^{\circ}=\frac{1}{0})$ $\Rightarrow 22x + 5 = 0$

Find the equation of line parallel to $y$-axis and

Notes on Straight lines

Concepts Used:

Straight lines

A straight line is a line having the shortest distance between two points.

A straight line can be represented as an equation in various forms, as show in the image below:

The following are the many forms of the equation of the line that are presented in straight line-

1. Slope – Point Form

Assume P0(x0, y0) is a fixed point on a non-vertical line L with m as its slope. If P (x, y) is an arbitrary point on L, then the point (x, y) lies on the line with slope m through the fixed point (x0, y0) if and only if its coordinates fulfil the equation below.

y – y₀ = m (x – x₀)

2. Two – Point Form

Let's look at the line. L crosses between two places. P₁(x₁, y₁) and P₂(x₂, y₂) are general points on L, while P (x, y) is a general point on L. As a result, the three points P₁, P₂, and P are collinear, and it becomes

The slope of P₂P = The slope of P₁P₂, i.e.

$\frac{y-y_1}{x-x_1} = \frac{y_2-y_1}{x_2-x_1}$

Hence, the equation becomes:

y - y₁ =$ \frac{y_2-y_1}{x_2-x_1} (x-x1)$

3. Slope-Intercept Form

Assume that a line L with slope m intersects the y-axis at a distance c from the origin, and that the distance c is referred to as the line L's y-intercept. As a result, the coordinates of the spot on the y-axis where the line intersects are (0, c). As a result, the slope of the line L is m, and it passes through a fixed point (0, c). The equation of the line L thus obtained from the slope – point form is given by

y – c =m( x - 0 )

As a result, the point (x, y) on the line with slope m and y-intercept c lies on the line, if and only if

y = m x +c

Find the equation of line parallel to $y$-axis and drawn through the point of intersection of the line $x - 7y + 5 = 0$ and $3x + y = 0$.

The Correct Option is B

Solution and Explanation

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