The equation for this line would be y = 5/6x + 17/2
In order to find this, we first need to start with the slope. Perpendicular lines have opposite and reciprocal slopes. Therefore, to be perpendicular to a line with a -6/5 slope, our new line would need to have a 5/6 slope.
Next we use that along with the given point in slope intercept form to find the intercept.
y = mx + b
1 = 5/6(-9) + b
1 = -15/2 + b
17/2 = b
Now that we have the slope and the intercept, we can write the equation.
The slope of the given line = (-1/(-6/5))
= 5/6 It passes through;
(-9,1) Using the slope intercept form;
y - y1 =m(x-x2) y-1=5/6(x--9)
» y -1 = 5/6(x+9) Multiplying through by 6 gives
5y-5 = 5(x+9)
Expanding brackets we have; 6y-6 = 5x+45 6y-5x-51= 0
is the required equation.