Class10 ICSE Maths Important Questions Chapter Equation Of Line

Class 10 ICSE Maths Equation Of Line Important Questions

The general equation of a line in two variables of the first degree is represented as Ax + By +C = 0, A, B ≠ 0 where A, B and C are constants which belong to real numbers. When we represent the equation geometrically, we always get a straight line.s

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Important Questions

Board Questions

Equation Of Line Important Questions

Q.1 The line

3x / 5

2y / 3

+ 1 = 0 contains the the point (m, 2m - 1); calculate the value of m. Solution

Q2 The line segment joining A(2, 1) and B(5, -8) is trisected at the points P and Q. If P is closer to point A and lies on the line 2x - y + k = 0, find the value of k Solution

Q3 Find the slope of the line passing through the points A (-2, 3) and B (2, 7) Also find:
(i) the inclination of the line AB,
(ii) slope of the line parallel to AB,
(iii) slope of the line perpendicular to AB. Solution

Q4 Given the points A (2, 3), B (-5, 0) and C (-2, a) are collinear. Find 'a'. Solution

Q5 Find the equation of a line :
(i) whose inclination is 45° and y-intercept is 5.
(ii) with inclination = 60° and passing through (-2, 5).
(iii) passing through the points (-3, 1) and (1, 5). Solution

Q6 Find the equation of the line whose x-intercept is 8 and y-intercept is -12. Solution

Q7 The equation of a line is 3x - 4y + 12 - 0. It meets the x-axis at point A and the y-axis at point B. Find :
(i) the co-ordinates of points A and B;
(ii) the length of intercept AB, cut by the line within the co-ordinate axes. Solution

Q8 Write down the equation of the line whose gradient is 3/2 and which passes through P, where P divides the line segment joining A (-2, 6) and B (3. -4) the ratio 2 : 3. Solution

Q9 A straight line passes through the point P(3, 2). It meets the x-axis at point A and the y-axis at point B. If

PA / PB

= -3, find the equation of the line that passes through the point P and is perpendicular to line AB. Solution

Q10 Find the equations of the lines passing through point (-2, 0) and equally inclined to the co-ordinate axes. Solution

Q11 The line through P(5, 3) intersects y-axis at Q.
(i) Write the slope of the line.
(ii) Write the equation of the line.
(iii) Find the co-ordinates of Q.

Solution

Q12 Given two straight lines 3x - 2y = 5 and 2x + ky + 7 = 0. Find the value of k at which the given lines are :
(i) parallel to each other.
(ii) perpendicular to each other. Solution