Q. 13

In each case find the points where the line meets the two axes.
         (i) 2x + y = 6
        (ii)  x - 2y = 4
        (iii) 2(x - 1) + 3y = 4
        (iv) y - 3x = 9
        (v)  2(x + 3) - 3(y + 1) = 0
        (vi) (x - y) - y + 4 = 0

Answer :

(i) 2x + y = 6
   For the point on the x-axis the value of y = 0.
   Substituting for y = 0 in the equation,
   2x + 0 = 6     ⇒ 2x = 6      ⇒   x = 3     ∴ The point where the line 2x + y = 6 ill touch the x-axis is (3, 0).
   For the point on the y-axis the value of x = 0.
   Substituting for x = 0 in the equation,
   2 × 0 + y = 6                ⇒ y = 6     ∴ The point where the line 2x+y=6 will touch the y-axis is (0, 6).
(ii) x - 2y = 4
    For the point on the x-axis the value of y= 0.
    Substituting for y= 0 in the equation,
    x - 2× 0 = 4           ⇒ x = 4      ∴ The point where the line x - 2y = 4 will touch the x-axis is (4, 0).
    For the point on the y-axis the value of x = 0.
    Substituting for x = 0 in the equation,
    0 - 2y = 4      ⇒ - 2y = 4          ⇒ y == -2      ∴ The point where the line x = -2, y = 4 will touch the y-axis is (0, -2).
(iii) 2(x-1) + 3y = 4
     For the point on the x-axis the value of y= 0.
     Substituting for y= 0 in the equation,
     2(x-1) + 3 × 0 = 4         ⇒ 2x -2 + 0 = 4            Þ 2x = 4 + 2 = 6                   ⇒ x = = 3       ∴ The point where the line 2(x - 1) + 3y = 4 will touch the x-axis is (3, 0).
     For the point on the y-axis the value of x = 0.
     Substituting for x = 0 in the equation,
     2(0 - 1) + 3y = 4          Þ -2 + 3y = 4                  ⇒ 3y = 4 + 2 = 6                    ⇒ y = = 2       ∴ The point where the line 2(x-1) + 3y = 4 will touch the y-axis is (0, 2).
(iv) y - 3x = 9
     For the point on the x-axis the value of y = 0.
     Substituting for y = 0 in the equation,
     0 -3x = 9       ∴ -3x = 9
          x = -3       ∴ The point where the line y -3x = 9 will touch the x-axis is (-3, 0).
     
     The point on the y-axis the value of x = 0.
     Substituting for x = 0 in the equation,
             y -3൰ = 9             ∴ y = 9       ∴ The point where the line 2x + y= 0 will touch the y-axis is (0, 9).
(v) 2(x + 3) - 3(y + 1) = 0
     For the point on the x-axis the value of y = 0.
     Substituting for y = 0 in the equation,
     2(x + 3)-3(0 + 1) = 0              ⇒ 2x + 6 - 3 = 0                            ⇒ 2x = -3                               ⇒ x = -
     ∴ The point where the line 2(x + 3)-3(y + 1)=0 will touch the x-axis is (-, 0).
     For the point on the y-axis the value of x = 0.
     Substituting for x = 0 in the equation,  
     2(0 + 3)-3(y + 1) = 0           ⇒ 0 + 6- 3y- 3 = 0                         ⇒ -3y = -3                             ⇒ y = 1       ∴ The point where the line 2(x + 3) - 3(y + 1) = 0 will touch the y-axis is (0, 1).
(vi) (x - y) -y + 4= 0
     For the point on the x-axis the value of y = 0.
     Substituting for y = 0 in the equation,
     (x - 0) - 0 + 4 = 0              ⇒ x + 4 = 0                    ⇒ x = -4       ∴ The point where the line (x - y) - y + 4 = 0 will touch the x-axis is (-4, 0).
     For the point on the y-axis the value of x= 0.
     Substituting for x = 0 in the equation,
     (0-y)-y+4 = 0            ⇒ -y - y = -4            Þ -2y = -4                   ⇒ y = 2       ∴ The point where the line (x - y) - y + 4 = 0 will touch the y-axis is (0, 2).

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