Mathematics
Find the equation of a line parallel to the line 2x + y – 7 = 0 and passing through the intersection of the lines x + y – 4 = 0 and 2x – y = 8.
Answer
Simultaneously solving equations :
⇒ x + y - 4 = 0 …….(1)
⇒ 2x - y = 8 ……..(2)
Solving equation (1), we get :
⇒ x = 4 - y ………..(3)
Substituting value of x from (3) in (2), we get :
⇒ 2(4 - y) - y = 8
⇒ 8 - 2y - y = 8
⇒ 8 - 3y = 8
⇒ 3y = 0
⇒ y = 0.
Substituting value of y in (3), we get :
⇒ x = 4 - 0 = 4.
Point of intersection = (4, 0).
Given,
Equation :
⇒ 2x + y - 7 = 0
⇒ y = -2x + 7
Comparing above equation with y = mx + c, we get :
⇒ m = -2.
We know that,
Slope of parallel lines are equal.
∴ Slope of line parallel to 2x + y - 7 = -2.
By point-slope formula,
Equation of line :
⇒ y - y1 = m(x - x1)
Thus, equation of line with slope = -2 and passing through (4, 0).
⇒ y - 0 = -2(x - 4)
⇒ y = -2x + 8
⇒ 2x + y - 8 = 0.
Hence, the equation of required line is 2x + y - 8 = 0.
Related Questions
Given that A(5, 4), B(–3, –2) and C(1, –8) are the vertices of a ΔABC. Find:
(i) the slope of median AD
(ii) the slope of altitude BM
Find the equation of the line parallel to the line 3x + 2y = 8 and passing through the point (0, 1).
A(–1, 3), B(4, 2) and C(3, –2) are the vertices of a triangle.
(i) Find the co-ordinates of the centroid G of the triangle.
(ii) Find the equation of the line through G and parallel to AC.
Find the equation of a line passing through the point P(–2, 1) and parallel to the line joining the points A(4, –3) and B(–1, 5).