Question

A line passes through the point , (−2,2) and has a slope of −5/2.

A line passes through the point , (2,−3) and has a slope of −5/2.

A line passes through the point , (−9,7) and has a slope of 4/3.

A line passes through the point , (2,−7) and has a slope of −5/2.

A line passes through the point , (8,−4) and has a slope of 3/4.

Please answer them all ;)

Answer 1

`$ (y -y_1) = m(x - x_1) $`

Explanation:

When a point and the slope of the line are given we use slope - one point form to determine the line of the equation.

Slope and One point form: y - y₁ = m(x - x₁)

where
`$ (x_1,y_1) $` is the point passing through the line and

`$ m $` is the slope of the line.

Point: (-2,2) Slope:
`$ (-5)/(2) $`

∴ (x₁ ,y₁) = (-2,2) & m =
`$ (-5)/(2) $`

Substituting we get:

y - 2 =
`$ (-5)/(2) (x + 2) $`

⇒ 2y - 4 = -5x - 10

⇒ 5x + 2y + 6 = 0

Point: (2,-3) Slope:
`$ (-5)/(2) $`

y + 3 =
`$ (-5)/(2) (x - 2) $`

⇒ 2y + 6 = -5x + 10

⇒ 5x + 2y - 4 = 0

Point: (-9,7) Slope:
`$ (4)/(3) $`

y - 7 =
`$ (4)/(3) (x + 9) $`

⇒ 3y - 21 = 4x + 36

⇒ 4x - 3y + 57 = 0

Point: (2,-7) Slope:
`$ (-5)/(2) $`

y + 7 =
`$ (-5)/(2) (x - 2) $`

⇒ 2y + 14 = -5x + 10

⇒ 5x + 2y + 4 = 0

Point: (8,4) Slope:
`$ (3)/(4) $`

y + 4 =
`$ (3)/(4) (x - 8) $`

⇒ 4y + 16 = 3x - 24

⇒ 3x - 4y -40 = 0