Determine the equation of the line that passes through the point (-2,1) and it is perpendicular to -x+4y-3=0

We'll write the equation of the line into the slope
intercept form:

y=mx+n, where m is the slope of the line
and n is the y intercept.

We need to put the equations
in this form to determine their slopes. We'll use the property of slopes of 2
perpendicular lines: the product of the values of the slopes of 2 perpendicular lines is
-1.

Let's suppose that the 2 slopes are m1 and
m2.

m1*m2=-1

We'll
determine m1 from the given equation of the line, that is perpendicular to the one with
the unknown equation.

The equation is
-x+4y-3=0.

We'll isolate 4y to the left side. For this
reason, we'll subtract -x - 3 both sides:

4y = x +
3

We'll divide by 4:

y = x/4 +
3/4

The slope m1 =
1/4.

(1/2)*m2=-1

m2=-4

We
also know that the line passes through the point (-2,1), so the equation of a line that
passes throuh a given point and it has a known slope
is:

(y-y1)=m(x-x1)

(y-1)=(-4)*(x+2)

We'll
remove the brackets and we'll move all terms to one side:

y
- 1 + 4x + 8 = 0

We'll combine like terms and
we'll get the equation of the requested line: y + 4x + 7 =
0