Write an equation of the line passing through (-6, 1) that is perpendicular to the line 2x -5y = 2
a. in point slope form
b. in standard form

y= -5/2 x + 14 (point slope form)

2y+5x=28 (standard form)

Step-by-step explanation:

Perpendicular lines met the following condition

m1*m2=-1 (the product of their slopes is -1)

To obtain m2, the slope of our desired line lets first re arrange the equation of the first line. 2x-5y=2, so. 2x-2=5y.

Isolating y, leads the following, result: y= 2/5 x - 2/5

m1=2/5

m2 is =-5/2

The equation of our desired line is the following

y=mx+b, we have m, which is -5/2, but still need to find value for b.

Lets now evaluate the above equation in the given point (-6,1).

1=-6 * -5/2 + b.

b=14.

Now we can say the equation that our desired line is

y= -5/2 x + 14 (point slope form)

Or... If we group variables 'x' and 'y' together

y+5/2 x = 14, we want integer coefficients, so lets multiply this expression by 2, to obtain the following:

2y+5x=28