Question

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

Answer 1

Answer:

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

Step-by-step 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: $\frac{-5}{2}$

∴ (x₁ ,y₁) = (-2,2) & m = $\frac{-5}{2}$

Substituting we get:

y - 2 = $\frac{-5}{2} (x + 2)$

⇒ 2y - 4 = -5x - 10

⇒                                         5x + 2y + 6 = 0

Point: (2,-3) Slope: $\frac{-5}{2}$

y + 3 = $\frac{-5}{2} (x - 2)$

⇒ 2y + 6 = -5x + 10

⇒                                         5x + 2y - 4 = 0

Point: (-9,7) Slope: $\frac{4}{3}$

y - 7 = $\frac{4}{3} (x + 9)$

⇒ 3y - 21 = 4x + 36

⇒                                        4x - 3y + 57 = 0

Point: (2,-7) Slope: $\frac{-5}{2}$

y + 7 = $\frac{-5}{2} (x - 2)$

⇒ 2y + 14 = -5x + 10

⇒                                        5x + 2y + 4 = 0

Point: (8,4) Slope: $\frac{3}{4}$

y + 4 = $\frac{3}{4} (x - 8)$

⇒ 4y + 16 = 3x - 24

⇒                                        3x - 4y -40 = 0