Question

1.) Write the equation of the line perpendicular to the line x - 5y = -10 and passing through the point (2,5).

2.) Write the equation of the line parallel to the line 10x - 5y = 8 and passing through the point (2,4).

3.) Write the equation of the line parallel to the line 4x + y = -1 and passing through the point (5,0).

4.) Write the equation of the line parallel to the line 4x + 2y = 5 and passing through the point (-3,5).

5.) Write the equation of the line perpendicular to the line x - 3y = 9 and passing through the point (3,5).

Answer 1

1. x - 5y = -10
- x - x
-5y = -x - 10
-5 -5
y = ¹/₅x + 2

y - y₁ = m(x - x₁)
y - 5 = -5(x - 2)
y - 5 = -5(x) + 5(2)
y - 5 = -5x + 10
+ 5 + 5
y = -5x + 15

2. 10x - 5y = 8
- 10x - 10x
-5y = -10x + 8
-5 -5
y = 2x - 1³/₅

y - y₁ = m(x - x₁)
y - 4 = 2(x - 2)
y - 4 = 2(x) - 2(2)
y - 2 = 2x - 4
+ 2 + 2
y = 2x - 2

3. 4x + y = -1
- 4x -4x
y = -4x - 1

y - y₁ = m(x - x₁)
y - 0 = -4(x - 5)
y - 0 = -4(x) + 4(5)
y - 0 = -4x + 20
+ 0 + 0
y = -4x + 20

4. 4x + 2y = 5
- 4x - 4x
2y = -4x + 5
2 2
y = -2x + 2¹/₂

y - y₁ = m(x - x₁)
y - 5 = -2[x - (-3)]
y - 5 = -2(x + 3)
y - 5 = -2(x) - 2(3)
y - 5 = -2x - 6
+ 5 + 5
y = -2x + 1

5. x - 3y = 9
- x - x
-3y = -x + 9
-3 -3
y = ¹/₃x - 3

y - y₁ = m(x - x₁)
y - 5 = -3(x - 3)
y - 5 = -3(x) + 3(3)
y - 5 = -3x + 9
+ 5 + 5
y = -3x + 14

Answer 2

write the equation in y = mx + b.
5Y = -10-x
y=-2-x/5
y=-1/5x-2
the slope = -1/5

put new slope from step 3 and a point into y = mx + b to find b.
5 = (2)(-1/5) + b
5=-2/5+b
5+2/5=b
25+2/5=b
27/5=b
13.5=b
Y = -1/5+13.5