Algebra/Math Homework Help?? Need Really quick Thank You So Much!!?

Question

1.Write an equation for the line that is perpendicular to the line y = 4x + 5 and that passes through the point (0, −3)
2.the coordinates of the vertices of WHY are W(0, 0), H(8, 3), and Y(2, 9). Find the equation of the line containing Meadian WO
3.Find the equation of the perpendicular bisector of side HY
4.Find the equation of the line containing altitude HT
Write an equation for the line through each pair of points
5.(1,2)(3,4)
6.(1,2)(3,-4)
7.(-1,-2)(-6,-4)

Answer 1

1). Given that equation is y = 4x + 5

This equation compare to y = mx + c

Here slope m = 4

perpendicular slope is - m = -4

passes through the point is(x₁, y₁) = (0, -3)

Note : The perpendicular line equation is (y - y₁) = - m(x - x₁)

There fore

(y - (-3)) = - 4 (x - 0)

y + 3 = - 4x

Add 4x to each side

y + 3 + 4x = - 4x + 4x

Simplify

4x + y + 3 = 0

5). (1, 2)(3, 4)

Note : Line equation formula is (y - y₁) = [(y₂ - y₁) / (x₂ - x₁)](x - x₁)

(x₁, y₁) = (1, 2) and (x₂, y₂) = (3, 4)

The line equation is (y - 2) = [(4 - 2)/ (3 - 1)](x - 1)

Simplify

(y - 2) = [( 2 ) / ( 2) ](x - 1)

(y - 2) = (x - 1)

Add 2 to each side

y - 2 + 2 = x - 1 + 2

y = x + 1

Subtract y from each side.

y - y = x + 1 - y

0 = x - y + 1

There fore

x - y + 1 = 0

6). (1, 2)(3, -4)

Note : Line equation formula is (y - y₁) = [(y₂ - y₁) / (x₂ - x₁)](x - x₁)

(x₁, y₁) = (1, 2) and (x₂, y₂) = (3, -4)

The line equation is (y - 2) = [(- 4 - 2)/(3 -1)](x - 1)

Simplify

(y - 2) = [( -6 ) / ( 2)](x - 1)

(y - 2) = (-3) (x - 1)

(y - 2) = -3x + 3

Add 3x to each side

y - 2 + 3x = -3x + 3 + 3x

y - 2 + 3x = 3

Subtract 3 from each side.

y - 2 + 3x - 3 = 3 - 3

y + 3x - 5 = 0

There fore

3x + y -5 = 0

7). (-1, -2)(-6, -4)

Note : Line equation formula is (y - y₁) = [(y₂ - y₁) / (x₂ - x₁)](x - x₁)

(x₁, y₁) = (-1, -2) and (x₂, y₂) = (-6, -4)

The line equation is (y -(- 2)) = [(- 4 -(- 2))/(-6 -(-1))](x - (-1))

Simplify

(y + 2) = [( -4 + 2 ) / ( -6 + 1)](x + 1)

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

(y + 2) = [2/5] (x + 1)

Multiply each side by 5.

5(y + 2) =  5 [2/5] (x + 1)

5y + 10 = 2 (x + 1)

5y + 10 = 2 x + 2

Subtract 5y from each side.

5y + 10 - 5y = 2 x + 2 - 5y

Simplify

10 = 2x - 5y + 2

Subtract 10 from each side.

10 - 10 = 2x - 5y + 2 - 10

0 = 2x - 5y -8

There fore

 2x - 5y - 8 = 0

Answer 2

2) The vertices are W(0, 0), H(8, 3) and Y(2, 9).

Median from the point W bisects HY at O.

Therefore midpoint point of HY is the bisecting point.

Therefore midpoint point of HY = ( (8+2)/2 , (3+9)/2 ) = (10/2, 12/2) = (5, 6).

The equation of the line WO is y - y₁ = [(y₂ - y₁ ) / (x₂ - x₁ )] (x - x₁ ) where W(0, 0) = (x₁, y₁) and O(5, 6) = (y₂, y₁)

y - 0 = [(6 - 0) / (5 - 0)] (x - 0)

y = 6/5 x

5y = 6x

6x - 5y = 0.

The equation of the median MO is 6x - 5y = 0.