Can you please help me with a slope formula equation?

Question

my teacher graded my homework and gave it back to me and she marked this question wrong.

the question says: write an equation in slope intercept form for the line that contains the given point and is PERPENDICULAR to y=2x-4 and passes through (-2,5)

Answer 1

 y = 2x - 4

The slope of the above equation is m1 = 2

If two lines are perpendicular then their slopes are opposite reciprocals

So , the slope of the line perpendicular to the line y = 2x - 4 is   m = -1/2

Now  the line equation contains slope m= -1/2 and passes through (-2, 5) is

 (y - y1) = m (x - x1)

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

⇒ y - 5 =  - 1/2 (x + 2)

⇒ 2y - 10 = -( x +2 )

⇒ 2y - 10 = -x - 2

    x + 2y -8 = 0

So, the line equation perpendicular to line y = 2x - 4   is x + 2y -8 = 0

Comments

The equation in slope intercept form is y = -1/2x + 4.

Answer 2

The equation is y = 2x - 4 and point is (-2, 5)

Compare the equation with slope - intercept form y = m₁x + b.

So, m₁ = 2.

If two lines are perpendicular, then their slopes are negative reciprocals of one another or product of the slopes is equal to -1.

So, perpendicular slope m₂ = -1/m₁ = -1/2.

You know the slope and a point on the line, so use the point - slope form with (x₁,y₁) = (-2, 5) to write  equation of the line.

(y - y₁) = m₂(x - x₁)

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

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

Apply distributive property: a(b + c) = ab + ac.

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

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

Add 5 to each side.

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

y = (-1/2)x + 4

The equation is y  = (-1/2)x + 4.