Respuesta :
Answer:
[tex]$ (y -y_1) = m(x - x_1) $[/tex]
Step-by-step explanation:
When a point and the slope of the line are given we use slope - one point form to determine the line of the equation.
Slope and One point form: y - y₁ = m(x - x₁)
where [tex]$ (x_1,y_1) $[/tex] is the point passing through the line and
[tex]$ m $[/tex] is the slope of the line.
Point: (-2,2) Slope: [tex]$ \frac{-5}{2} $[/tex]
∴ (x₁ ,y₁) = (-2,2) & m = [tex]$ \frac{-5}{2} $[/tex]
Substituting we get:
y - 2 = [tex]$ \frac{-5}{2} (x + 2) $[/tex]
⇒ 2y - 4 = -5x - 10
⇒ 5x + 2y + 6 = 0
Point: (2,-3) Slope: [tex]$ \frac{-5}{2} $[/tex]
y + 3 = [tex]$ \frac{-5}{2} (x - 2) $[/tex]
⇒ 2y + 6 = -5x + 10
⇒ 5x + 2y - 4 = 0
Point: (-9,7) Slope: [tex]$ \frac{4}{3} $[/tex]
y - 7 = [tex]$ \frac{4}{3} (x + 9) $[/tex]
⇒ 3y - 21 = 4x + 36
⇒ 4x - 3y + 57 = 0
Point: (2,-7) Slope: [tex]$ \frac{-5}{2} $[/tex]
y + 7 = [tex]$ \frac{-5}{2} (x - 2) $[/tex]
⇒ 2y + 14 = -5x + 10
⇒ 5x + 2y + 4 = 0
Point: (8,4) Slope: [tex]$ \frac{3}{4} $[/tex]
y + 4 = [tex]$ \frac{3}{4} (x - 8) $[/tex]
⇒ 4y + 16 = 3x - 24
⇒ 3x - 4y -40 = 0
