Question

find equation of line passing through point of intersection of lines x+y=0 and 2x-y=9 and through point (2,5)​

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

$m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{5+3}{2-3}\\\\m=-8$

The point-slope form of a line is given by

$y-y_1=m(x-x_1)\\\\y+3=-8(x-3)\\\\y+3=-8x+24\\\\y=-8x+21$

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.​

https://brainly.in/question/13398071

Answer 2

Step-by-step explanation:

Above is you solution of the answer.