Frank solutions for Mathematics - Part 2 [English] Class 10 ICSE chapter 13 - Equation of A Straight Line [Latest edition]

Find if the following points lie on the given line or not:
 (1,3) on the line 2x + 3y = 11

Find if the following points lie on the given line or not:

(5,3) on the line 3x - 5y + 5 = 0

Find if the following points lie on the given line or not:

(2,4) on the line y = 2x - 1

Find if the following points lie on the given line or not:

(-1, 5) on the line 3x = 2y -15

Find if the following points lie on the given line or not:

(7, -2) on the line 5x + 7y = 11

Find the value of m if the line 2x + 5y + 12 = 0 passes through the point
( 4,m ).

Find the value of p if the line 3y = 5x - 7 passes through the point (p,6).

Find the value of a if the line 4 x = 11 - 3y passes through the point (a, 5)

The line y = 6- `(3"x")/2` passes through the point (r,3). Find the value of r. 

The line `(3 + 5"y")/2 = (4"x" - 7)/3` passes through the point ( 1, k). find the value of k

The line 4x + 3y = 11 bisects the join of ( 6,m) and (p,9). Find the value of m.

The line 2x - 5y + 31 = 0 bisects the join of (-4,5) and (P, 9). Find the value of p.

The line segment formed by the points (3, 7) and (-7, z) is bisected by the line 3x + 4y =18. Find the value of z.

The line 5x - 3y +1 = 0 divides the join of (2,m) and (7,9) in the ratio 2: 3. Find the value of m.

The line 7x - 8y = 4 divides join of (-8,-4) and (6,k) in the ratio of 2 : 5. Find the value of k.

The line 5x + 3y = 25 divides the join of (b,4) and (5, 8) in the ratio of 1 : 3. Find the value of b.

P is a point on the line segment AB dividing it in the ratio 2 : 3. If the coordinates of A and Bare (-2,3) and (8,8), find if Plies on the line 7x - 2y =4.

L is a point on the line segment PQ dividing it in the ratio 1 : 3. If the coordinates of P and Q are (3, 7) and ( 11,-5) respectively, find if L lies on the line 2x + 5y = 20.

The line segment formed by two points A (2,3) and B (5, 6) is divided by a point in the ratio 1 : 2. Find, whether the point of intersection lies on the line 3x - 4y + 5 = 0.

Find the slope of a line, correct of two decimals, whose inclination is 60°

Find the slope of a line, correct of two decimals, whose inclination is 50°

Find the slope of a line, correct of two decimals, whose inclination is 45°

Find the slope of a line, correct of two decimals, whose inclination is 75°

Find the slope of a line, correct of two decimals, whose inclination is 30°

Find the inclination of a line whose gradient is 0.4663

Find the inclination of a line whose gradient is 1.4281 

Find the inclination of a line whose gradient is 3.0777

Find the inclination of a line whose gradient is 5.6713

Find the inclination of a line whose gradient is  0.5317

Find the slope of a line passing through the given pair of points (2,5) and (-1,8)

Find the slope of a line passing through the given pair of points  (3,7) and (5,13)

Find the slope of a line passing through the given pair of points (-5,-1) and (-9,-7)

Find the slope of a line passing through the given pair of points (9,-2) and (-5,5)

Find the slope of a line passing through the given pair of points (0,5) and (5,0)

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

(²m²,2am) and (p²m²,2pm)

Find the slope of a line passing through the following pair of points 

(5pq,p2q) and (5qr,qr²)

Find the slope of a line parallel to the given line 3x-2y = 5

Find the slope of a line parallel to the given line x +3y = 7

Find the slope of a line parallel to the given line 5x-y = 10

Find the slope of a line parallel to the given line 4x-2y = 3

Find the slope of a line parallel to the given line 5x + 2y = 11

Find the value of a line perpendicular to the given line  2x-3y = 4

Find the value of a line perpendicular to the given line  5x+2y-9 = 0

Find the value of a line perpendicular to the given line 3x+4y = 13

Find the value of a line perpendicular to the given line  x-4y = 8

Find the value of a line perpendicular to the given line 9x-3y = 5

Find the slope of a line passing through the  points (x, 9) and (12, 6) is `(-1)/3 = ("y"_2 - "y"_1)/("x"_2 - "x"_1)`

Find m if the slope of the line passing through the point (-7,5) and (2,m) is `1/3`

Find the value of a line parallel to the following line:

x = `"y"/2` - 5

Find the value of a line parallel to the following line:

x = `3"y"/2` + 2

Find the value of a line parallel to the following line:

`(3"y")/4 + (5"y")/2 = 7`

Find the value of a line parallel to the following line:

`"x"/4 +"y"/3` = 1

Find the value of a line parallel to the following line: 

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

Find the slope of a line perpendicular to the foloowing line `"x"/2 + "y"/3 = 4/3`

Find the slope of a line perpendicular to the foloowing line  x - `(3"y")/2 + 1 = 0`

Find the slope of a line perpendicular to the foloowing line  `(3"x")/4 -"y" = 5`

Find the slope of a line perpendicular to the foloowing line 3x - 5y = 9

Find the slope of a line perpendicular to the foloowing line 4x + y = 7

Find the slope and the y-intercept of the following line 5x - 2y = 6

Find the slope and the y-intercept of the following line 3x + y = 7

Find the slope and the y-intercept of the following line 4y = 5x - 8

Find the slope and the y-intercept of the following line 2x + 3y = 12

Find the equation of a line whose slope and y-intercept are m = `(-6)/5`, c = 3

Find the equation of a line whose slope and y-intercept are m = `2/3`, c = -2

Find the equation of a line whose slope and y-intercept are m = `(-1)/2`, c = 5

Find the equation of a line whose slope and y-intercept are m = -3, c = -1

Find the equation of a line whose slope and y-intercept are m = 2, c = -5

Find the equation of a line passing through (2,5) and making and angle of 30° with the positive direction of the x-axis.

Find the equation of a line passing through (3,7) and making an angle of 60° with the negative direction of the x-axis.

Find the equation of a line passing through (8,3) and making an angle of 45° with the positive direction of the y-axis.

Find the equation of a line passing through (2,9)  and parallel to the line 3x + 4y = 11

Find the equation of a line passing through (-5,-1) and perpendicular to the 3x + y = 9

Find the equation of the perpendicular bisector of AB if the coordinates of A and B are (2,6) and ( 4,6).

Find the equation of a line perpendicular to the join of A(3,5) and B(-1,7) if it passes through the midpoint of AB.

Find the equation of a line passing through the intersection of x + 3y = 6 and 2x - 3y = 12 and parallel to the line 5x + 2y = 10

Find the equation of a line passing through the intersection of x + 2y + 1= 0 and 2x - 3y = 12 and perpendicular to the line 2x + 3y = 9

Find the equation of a line passing through the intersection of `"x"/10 + "y"/5` = 14 and `"x"/8 + "y"/6` = 15 and perpendicular to the line x - 2y = 5

The lines px + 5y + 7 = 0 and 2y = 5x - 6 are perpendicular to ach other. Find p.

The  lines 3x - 2y + 4 = 0 and 3x + my + 6 = 0 are parallel to each other . Find m.

Find the relation connecting p and q, if the lines py = 2x + 5 and qx + 3y = 2 are parallel to each other.

Find the relation connecting a and b, if the lines ay = 2x + 4 and 4y + bx = 2 are perpendicular to each other.

P(5,3), Q(-4,7) and R(8,3) are he vertices of a traingles. Find the equation of the median of the traiangle from p.

A(8,5), B (-2,1) and C(5,4) are the vertices of a triangle. Find the equation of the median of the traingle through C.

ABCD is rhombus. The coordinates of A and C ae (3,7) and (9,15). Find the equation of BD.

ABCD is a square. The cooordinates of B and D are (-3, 7) and (5, -1) respectively. Find the equation of AC.

The coordinates of two points P and Q are (0,4) and (3,7) respectively. Find

(i) The gradient of PQ

(ii) the equation of PQ

(iii) the coordinates of the point where the line AB intersects the X-axis.

X(4,9), Y(-5,4) and Z(7,-4) are the vertices of a triangle. Find the equation of the altitude of the triangle through X.