English

Equation of the line passing through (1, 2) and parallel to the line y = 3x – 1 is ______. - Mathematics

Advertisements
Advertisements

Question

Equation of the line passing through (1, 2) and parallel to the line y = 3x – 1 is ______.

Options

  • y + 2 = x + 1

  • y + 2 = 3 (x + 1)

  • y – 2 = 3 (x – 1)

  • y – 2 = x – 1

MCQ
Fill in the Blanks
Advertisements

Solution

Equation of the line passing through (1, 2) and parallel to the line y = 3x – 1 is y – 2 = 3 (x – 1).

Explanation:

Given equation is y = 3x – 1

Slope = 3

Slope of the line passing through the given point (1, 2) and parallel to the given line = 3

So, the equation of the required line is y – 2 = 3(x – 1)

shaalaa.com
  Is there an error in this question or solution?
Chapter 10: Straight Lines - Exercise [Page 182]

APPEARS IN

NCERT Exemplar Mathematics [English] Class 11
Chapter 10 Straight Lines
Exercise | Q 34 | Page 182

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

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


Without using distance formula, show that points (–2, –1), (4, 0), (3, 3) and (–3, 2) are vertices of a parallelogram.


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.

Find the value of p so that the three lines 3x + y – 2 = 0, px + 2y – 3 = 0 and 2x – y – 3 = 0 may intersect at one point.


Find the slope of the lines which make the following angle with the positive direction of x-axis:

\[\frac{2\pi}{3}\]


Find the slope of the lines which make the following angle with the positive direction of x-axis: 

\[\frac{3\pi}{4}\]


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

(3, −5), and (1, 2)


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

Through (6, 3) and (1, 1); through (−2, 5) and (2, −5)


What is the value of y so that the line through (3, y)  and (2, 7) is parallel to the line through (−1, 4) and (0, 6)?


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.


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


Show that the perpendicular bisectors of the sides of a triangle are concurrent.


Find the equations of the altitudes of a ∆ ABC whose vertices are A (1, 4), B (−3, 2) and C (−5, −3).


If the image of the point (2, 1) with respect to a line mirror is (5, 2), find the equation of the mirror.


Find the equation of the right bisector of the line segment joining the points (3, 4) and (−1, 2).


Find the angles between the following pair of straight lines:

x − 4y = 3 and 6x − y = 11


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


If θ is the angle which the straight line joining the points (x1, y1) and (x2, y2) subtends at the origin, prove that  \[\tan \theta = \frac{x_2 y_1 - x_1 y_2}{x_1 x_2 + y_1 y_2}\text { and } \cos \theta = \frac{x_1 x_2 + y_1 y_2}{\sqrt{{x_1}^2 + {y_1}^2}\sqrt{{x_2}^2 + {y_2}^2}}\].


The medians AD and BE of a triangle with vertices A (0, b), B (0, 0) and C (a, 0) are perpendicular to each other, if


The reflection of the point (4, −13) about the line 5x + y + 6 = 0 is  


The line passing through (– 2, 0) and (1, 3) makes an angle of ______ with X-axis.


If the line joining two points A(2, 0) and B(3, 1) is rotated about A in anticlock wise direction through an angle of 15°. Find the equation of the line in new position.


If the slope of a line passing through the point A(3, 2) is `3/4`, then find points on the line which are 5 units away from the point A.


A ray of light coming from the point (1, 2) is reflected at a point A on the x-axis and then passes through the point (5, 3). Find the coordinates of the point A.


If one diagonal of a square is along the line 8x – 15y = 0 and one of its vertex is at (1, 2), then find the equation of sides of the square passing through this vertex.


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)`


If the equation of the base of an equilateral triangle is x + y = 2 and the vertex is (2, – 1), then find the length of the side of the triangle.


A variable line passes through a fixed point P. The algebraic sum of the perpendiculars drawn from the points (2, 0), (0, 2) and (1, 1) on the line is zero. Find the coordinates of the point P.


P1, P2 are points on either of the two lines `- sqrt(3) |x|` = 2 at a distance of 5 units from their point of intersection. Find the coordinates of the foot of perpendiculars drawn from P1, P2 on the bisector of the angle between the given lines.


Slope of a line which cuts off intercepts of equal lengths on the axes is ______.


The equation of the straight line passing through the point (3, 2) and perpendicular to the line y = x is ______.


The points (3, 4) and (2, – 6) are situated on the ______ of the line 3x – 4y – 8 = 0.


The line `x/a + y/b` = 1 moves in such a way that `1/a^2 + 1/b^2 = 1/c^2`, where c is a constant. The locus of the foot of the perpendicular from the origin on the given line is x2 + y2 = c2.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×