Answer: 2y + 3x = -8.
Step-by-step explanation:
Given our first equation 2x-3y =13, we rewrite in the form of equation of a line, i.e y = mx + c
Where m is the slope of the line and c is the intersection on y axis.
By rewriting, we have...
3y= 2x-13
y= 2x/3 - 13/3.
m= 2/3, c= -13/3.
For two perpendicular lines, the product of their gradients is -1
i.e
m¹ * m² = -1
Hence m² = -1 * 3/2
m² = -3/2.
Hence, to get the equation of the line passing through the point (-6,5) we first find the intersection when x=0 given as
[Y-c]/[x-0] = -3/2
2y - 2c = -3x
2(5) - 2c =- 3(-6)
10-18= 2c
C = -8/2
C= -4
Then the equation is given as
y = mx + c
y = [-3/2]x - 4
2y= -3x - 8
2y + 3x = -8.
