A rule in coordinate geometry you have to know.... 1..When two lines are perpendicular to each other then the product of their gradient is - 1...i.e(m¹×m²=-1)
2.. When two lines are parallel to each other their gradient is the same I.e m¹ =m²...
This question will make use of the first rule...
The second straight line was given to be y =3x+2.. Generally a straight line has the formula y=mx+c(where m=gradient, c=intercept)
So in y=3x+2(the gradient here is 3)
Now from the first rule the product of this line and the line of coordinates (3,5) is - 1..
:- m1*m2=-1
3×m2=-1
m2 = - 1/3....this is the gradient of the line with coordinate (3,5)
Gradient = (y-y₁)/(x-x₁)
-1/3 = (y-5)/(x-3)
Cross multiply you'll have
-1(x-3)=3(y-5)
-x+3=3y-15
3y+x-15-3=0
3y+x-18=0........... Checked....
Or 3y+x=18......
Hope this helped....?
