English

Reduce the following equation into slope-intercept form and find their slopes and the y-intercepts. 6x + 3y – 5 = 0 - Mathematics

Advertisements
Advertisements

Question

Reduce the following equation into slope-intercept form and find their slopes and the y-intercepts.

6x + 3y – 5 = 0

Sum

Solution

The given equation is 6x + 3y – 5 = 0.

It can be written as

y = `1/3(-6"x" + 5)`

y = `-2"x" + 5/3` ........(1)

This equation is of the form y = mx + c, where m =  −2 and c = `5/3`.

Therefore, equation (1) is in the slope-intercept form, where the slope and the y-intercept are −2 and `5/3` respectively.

shaalaa.com
  Is there an error in this question or solution?
Chapter 10: Straight Lines - Exercise 10.3 [Page 227]

APPEARS IN

NCERT Mathematics [English] Class 11
Chapter 10 Straight Lines
Exercise 10.3 | Q 1.2 | Page 227

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Reduce the following equation into normal form. Find their perpendicular distances from the origin and angle between perpendicular and the positive x-axis.

`x – sqrt3y + 8 = 0`


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


In the triangle ABC with vertices A (2, 3), B (4, –1) and C (1, 2), find the equation and length of altitude from the vertex A.


Find the equation of a line making an angle of 150° with the x-axis and cutting off an intercept 2 from y-axis.


Find the equation of a line which makes an angle of tan−1 (3) with the x-axis and cuts off an intercept of 4 units on negative direction of y-axis.


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


Find the equation of a line for  p = 5, α = 60°.


Find the equation of a line for p = 8, α = 300°.


Find the equation of the straight line on which the length of the perpendicular from the origin is 2 and the perpendicular makes an angle α with x-axis such that sin α = \[\frac{1}{3}\].


The length of the perpendicular from the origin to a line is 7 and the line makes an angle of 150° with the positive direction of Y-axis. Find the equation of the line.


Find the equation of the straight line which makes a triangle of area \[96\sqrt{3}\] with the axes and perpendicular from the origin to it makes an angle of 30° with Y-axis.


Find the equation of a straight line on which the perpendicular from the origin makes an angle of 30° with x-axis and which forms a triangle of area \[50/\sqrt{3}\] with the axes.


Reduce the equation\[\sqrt{3}\] x + y + 2 = 0 to intercept form and find intercept on the axes.


Put the equation \[\frac{x}{a} + \frac{y}{b} = 1\] to the slope intercept form and find its slope and y-intercept.


Show that the origin is equidistant from the lines 4x + 3y + 10 = 0; 5x − 12y + 26 = 0 and 7x + 24y = 50.


Find the values of θ and p, if the equation x cos θ + y sin θ = p is the normal form of the line \[\sqrt{3}x + y + 2 = 0\].


Find the point of intersection of the following pairs of lines:

\[y = m_1 x + \frac{a}{m_1} \text { and }y = m_2 x + \frac{a}{m_2} .\]


Find the area of the triangle formed by the line x + y − 6 = 0, x − 3y − 2 = 0 and 5x − 3y + 2 = 0.


Show that the area of the triangle formed by the lines y = m1 x, y = m2 x and y = c is equal to \[\frac{c^2}{4}\left( \sqrt{33} + \sqrt{11} \right),\] where m1, m2 are the roots of the equation \[x^2 + \left( \sqrt{3} + 2 \right)x + \sqrt{3} - 1 = 0 .\]


Find the orthocentre of the triangle the equations of whose sides are x + y = 1, 2x + 3y = 6 and 4x − y + 4 = 0.


If the three lines ax + a2y + 1 = 0, bx + b2y + 1 = 0 and cx + c2y + 1 = 0 are concurrent, show that at least two of three constants a, b, c are equal.


If a, b, c are in A.P., prove that the straight lines ax + 2y + 1 = 0, bx + 3y + 1 = 0 and cx + 4y + 1 = 0 are concurrent.


Find the equation of a line which is perpendicular to the line \[\sqrt{3}x - y + 5 = 0\] and which cuts off an intercept of 4 units with the negative direction of y-axis.


Find the equation of the straight line perpendicular to 2x − 3y = 5 and cutting off an intercept 1 on the positive direction of the x-axis.


Find the equation of the straight line which has y-intercept equal to \[\frac{4}{3}\] and is perpendicular to 3x − 4y + 11 = 0.


Find the projection of the point (1, 0) on the line joining the points (−1, 2) and (5, 4).


Find the values of α so that the point P (α2, α) lies inside or on the triangle formed by the lines x − 5y+ 6 = 0, x − 3y + 2 = 0 and x − 2y − 3 = 0.


Write the coordinates of the orthocentre of the triangle formed by the lines xy = 0 and x + y = 1.


Write the area of the figure formed by the lines a |x| + b |y| + c = 0.

 

The point which divides the join of (1, 2) and (3, 4) externally in the ratio 1 : 1


The centroid of a triangle is (2, 7) and two of its vertices are (4, 8) and (−2, 6). The third vertex is


Find the equation of the line where length of the perpendicular segment from the origin to the line is 4 and the inclination of the perpendicular segment with the positive direction of x-axis is 30°.


Find the equation of the straight line which passes through the point (1, – 2) and cuts off equal intercepts from axes.


For what values of a and b the intercepts cut off on the coordinate axes by the line ax + by + 8 = 0 are equal in length but opposite in signs to those cut off by the line 2x – 3y + 6 = 0 on the axes.


If the intercept of a line between the coordinate axes is divided by the point (–5, 4) in the ratio 1 : 2, then find the equation of the line.


Locus of the mid-points of the portion of the line x sin θ + y cos θ = p intercepted between the axes is ______.


Reduce the following equation into slope-intercept form and find their slopes and the y-intercepts.

x + 7y = 0


Reduce the following equation into normal form. Find their perpendicular distances from the origin and angle between perpendicular and the positive x-axis.

y − 2 = 0


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×