Question

9. Find the equation of line passing
through the point (2,5) and through
the intersection of the lines x+y=0
and 2x-y= 9.
O 8x+y-21=0
O 7x+y+31=0
O X-y-1=0
o
O 6x+5y-2=0​

Answer 1

The equation of the line is y=-8x+21

Step-by-step explanation:

The given equations are

x + y = 0...(i)

2x - y = 9...(ii)

Find the solution of this system of equation which will also gives us the intersection point.

Add (i) and (ii)

3x = 9

Divide both sides by 3

x = 3

Substitute the value of x in (i)

3 + y = 0

y = -3

Therefore, the intersection point of these lines is (3,-3).

Thus, the required line is passing through the points (3, -3) and (2,5)

Slope of the line is given by

The point-slope form of a line is given by

Therefore, the equation of the line is y=-8x+21

#Learn More:

Find the point of intersection of the line joining points (3,7) (2, -4) and of the line joining points (-3,7) (2, -4) and (4,6) (-5,–7). Also  find the point of intersection of these lines and also their intersection with the axis.​