What is the equation of the line (in y=mx+b form) that passes through (-3,1) and is perpendicular to the line 2x-5y=-17?

We need to find the line in the form (y= mx +
b).

Given the point (-3, 1) passes through the
line.

The, we will write the line equation in the slope
form.

==> y- y1= m (x-x1) where (x1,y1) is any point
passes through the line and m is the slope.

Then, we will
substitute the point.

==> ( y -1) = m
(x+3)

But, given the perpendicular line 2x-5y =
-17.

We know that the product of the slopes =
-1.

Let us determine the slope of the perpendicular
line.

==> 2x -5y =
-17

==> -5y = -2x -
17

==> y= (2/5)x
+17/5.

Then, the perpendicular slope is
2/5.

==> (2/5)* m =
-1

==> m =
-5/2

==> (y-1) = (-5/2)( x+
3)

==> y-1 = (-5/2)x -
15/2

==> y= (-5/2)x - 15/2 +
1

==> y= (-5/2)x -
13/2