English

Find the Slope of a Line Passing Through the Following Point: (−3, 2) and (1, 4)

Advertisements
Advertisements

Question

Find the slope of a line passing through the following point:

 (−3, 2) and (1, 4)

Answer in Brief
Advertisements

Solution

(−3, 2) and (1, 4)

Let m be the slope of the given line.

\[\therefore m = \frac{y_2 - y_1}{x_2 - x_1}\]

\[ \Rightarrow m = \frac{4 - 2}{1 + 3} = \frac{2}{4} = \frac{1}{2}\]

Hence, the slope of the line passing through the points (−3, 2) and (1, 4) is \[\frac{1}{2}\].

shaalaa.com
  Is there an error in this question or solution?
Chapter 23: The straight lines - Exercise 23.1 [Page 13]

APPEARS IN

R.D. Sharma Mathematics [English] Class 11
Chapter 23 The straight lines
Exercise 23.1 | Q 2.1 | Page 13

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Find the distance between P (x1, y1) and Q (x2, y2) when :

  1. PQ is parallel to the y-axis,
  2. PQ is parallel to the x-axis

Find the slope of a line, which passes through the origin, and the mid-point of the line segment joining the points P (0, –4) and B (8, 0).


Find the angle between the x-axis and the line joining the points (3, –1) and (4, –2).


Find the values of k for which the line (k–3) x – (4 – k2) y + k2 –7k + 6 = 0 is 

  1. Parallel to the x-axis,
  2. Parallel to the y-axis,
  3. Passing through the origin.

State whether the two lines in each of the following are parallel, perpendicular or neither.

Through (9, 5) and (−1, 1); through (3, −5) and (8, −3)


State whether the two lines in each of the following is parallel, perpendicular or neither.

Through (3, 15) and (16, 6); through (−5, 3) and (8, 2).


Using the method of slope, show that the following points are collinear A (16, − 18), B (3, −6), C (−10, 6) .


What can be said regarding a line if its slope is  zero ?


What can be said regarding a line if its slope is positive ?


Show that the line joining (2, −3) and (−5, 1) is parallel to the line joining (7, −1) and (0, 3).


Show that the line joining (2, −5) and (−2, 5) is perpendicular to the line joining (6, 3) and (1, 1).


Prove that the points (−4, −1), (−2, −4), (4, 0) and (2, 3) are the vertices of a rectangle.


The slope of a line is double of the slope of another line. If tangents of the angle between them is \[\frac{1}{3}\],find the slopes of the other line.


Consider the following population and year graph:
Find the slope of the line AB and using it, find what will be the population in the year 2010.


Find the angle between the X-axis and the line joining the points (3, −1) and (4, −2).


Find the value of x for which the points (x, −1), (2, 1) and (4, 5) are collinear.


Find the angle between X-axis and the line joining the points (3, −1) and (4, −2).


Find the equation of a straight line  with slope − 1/3 and y-intercept − 4.


Find the equation of the perpendicular to the line segment joining (4, 3) and (−1, 1) if it cuts off an intercept −3 from y-axis.


Find the equation of the strainght line intersecting y-axis at a distance of 2 units above the origin and making an angle of 30° with the positive direction of the x-axis.


Find the coordinates of the orthocentre of the triangle whose vertices are (−1, 3), (2, −1) and (0, 0).


The line through (h, 3) and (4, 1) intersects the line 7x − 9y − 19 = 0 at right angle. Find the value of h.


Find the image of the point (3, 8) with respect to the line x + 3y = 7 assuming the line to be a plane mirror.


Find the angles between the following pair of straight lines:

3x + y + 12 = 0 and x + 2y − 1 = 0


Find the angles between the following pair of straight lines:

3x + 4y − 7 = 0 and 4x − 3y + 5 = 0


Prove that the points (2, −1), (0, 2), (2, 3) and (4, 0) are the coordinates of the vertices of a parallelogram and find the angle between its diagonals.


Find the angle between the line joining the points (2, 0), (0, 3) and the line x + y = 1.


If two opposite vertices of a square are (1, 2) and (5, 8), find the coordinates of its other two vertices and the equations of its sides.


The equation of the line with slope −3/2 and which is concurrent with the lines 4x + 3y − 7 = 0 and 8x + 5y − 1 = 0 is


Find the equation of the straight line passing through (1, 2) and perpendicular to the line x + y + 7 = 0.


The equation of the line passing through (1, 2) and perpendicular to x + y + 7 = 0 is ______.


The intercept cut off by a line from y-axis is twice than that from x-axis, and the line passes through the point (1, 2). The equation of the line is ______.


Show that the tangent of an angle between the lines `x/a + y/b` = 1 and `x/a - y/b` = 1 is `(2ab)/(a^2 - b^2)`


Equations of diagonals of the square formed by the lines x = 0, y = 0, x = 1 and y = 1 are ______.


One vertex of the equilateral triangle with centroid at the origin and one side as x + y – 2 = 0 is ______.


If the vertices of a triangle have integral coordinates, then the triangle can not be equilateral.


The equation of the line through the intersection of the lines 2x – 3y = 0 and 4x – 5y = 2 and

Column C1 Column C2
(a) Through the point (2, 1) is (i) 2x – y = 4
(b) Perpendicular to the line (ii) x + y – 5
= 0 x + 2y + 1 = 0 is
(ii) x + y – 5 = 0
(c) Parallel to the line (iii) x – y –1 = 0
3x – 4y + 5 = 0 is
(iii) x – y –1 = 0
(d) Equally inclined to the axes is (iv) 3x – 4y – 1 = 0

The line which passes through the origin and intersect the two lines `(x - 1)/2 = (y + 3)/4 = (z - 5)/3, (x - 4)/2 = (y + 3)/3 = (z - 14)/4`, is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×