Question

Write the equation of the line through (−5,3) and:

a. Parallel to x = −1.
b. Perpendicular to x = −1.
c. Parallel to y = 3 / 5 x + 2.
d. Perpendicular to y = 3 / 5 x + 2.

Answer 1

a) x + y = -2

b) x - y = -8

c) 3x - 5y = -30

d) 5x + 3y = -16

Explanation:

Equation of line with slope m and passing through (x₁,y₁) is given by

y - y₁ = m ( x -x₁)

(x₁,y₁) = (−5,3)

a) Parallel to x = −1

Slope , m = -1

y - y₁ = m ( x -x₁)

y - 3 = -1 ( x -(-5))

y -3 = -x - 5

x + y = -2

b) Perpendicular to x = −1.

Slope of line x Slope of perpendicular line = -1

Slope of line x -1 = -1

Slope , m = 1

y - y₁ = m ( x -x₁)

y - 3 = 1 ( x -(-5))

y -3 = x + 5

x - y = -8

c) Parallel to y = 3 / 5 x + 2

Slope , m = 3/5

`y-y_1=m(x-x_1)\\\\y-3=(3)/(5)(x-(-5))\\\\5y-15=3x+15\\\\3x-5y=-30`

3x - 5y = -30

d) Perpendicular to y = 3 / 5 x + 2

Slope of line x Slope of perpendicular line = -1

Slope of line x 3/5 = -1

Slope , m = -5/3

`y-y_1=m(x-x_1)\\\\y-3=(-5)/(3)(x-(-5))\\\\3y-9=-5x-25\\\\5x+3y=-16`

5x + 3y = -16