Question:

Find equation of the line parallel to the line 3x−4y+2=03x - 4y + 2 = 0 and passing through the point (-2, 3).

Updated On: Oct 21, 2023
Hide Solution
collegedunia
Verified By Collegedunia

Solution and Explanation

The equation of the given line is
3x–4y+2=03x – 4y + 2 = 0

or y=3x4+24y = \frac{3x}{4} +\frac{ 2}{4}

y=3x4+12y=\frac{ 3x}{4} + \frac{1}{2}, which is of the form y=mx+cy = mx + c

∴ Slope of the given line=34\frac{3}{4}
It is known that parallel lines have the same slope. 

∴ Slope of the other line =m=34=m=\frac{3}{4}
Now, the equation of the line that has a slope of 34\frac{3}{4} and passes through the point (-2, 3) is
y–3=34(x–(−2))y – 3 = \frac{3}{4} (x – (-2))
4y– 12=3x+ 64y – 12 = 3x + 6
i.e,3x–4y +18=0i.e,3x – 4y + 18 = 0

Was this answer helpful?
0
0

Top Questions on Distance of a Point From a Line

View More Questions

Questions Asked in CBSE Class XI exam

View More Questions

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.

y−y1x−x1=y2−y1x2−x1\frac{y-y_1}{x-x_1} = \frac{y_2-y_1}{x_2-x_1}

Hence, the equation becomes:

y - y1 =y2−y1x2−x1(x−x1) \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