Answer: [tex]a)\quad y=\dfrac{4}{5}x+\dfrac{8}{5}[/tex] [tex]b)\quad y=\dfrac{1}{3}x+\dfrac{10}{3}[/tex]
Step-by-step explanation:
Use the Slope formula: [tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
and the Point-Slope formula: y - y₁ = m(x - x₁)
a) (-2, 0) and (3, 4)
[tex]m=\dfrac{0-4}{-2-3}\quad =\dfrac{-4}{-5}\quad =\dfrac{4}{5}[/tex]
Let (x₁, y₁) = (-2, 0)
y - y₁ = m(x - x₁)
[tex]y-0=\dfrac{4}{5}\bigg(x-(-2)\bigg)\\\\\\y\quad =\dfrac{4}{5}\bigg(x+2\bigg)\\\\\\\large\boxed{y\quad =\dfrac{4}{5}x+\dfrac{8}{5}}[/tex]
b) m = 1/3 (x₁, y₁) = (2, 4)
y - y₁ = m(x - x₁)
[tex]y-4=\dfrac{1}{3}\bigg(x-2\bigg)\\\\\\y-4 =\dfrac{1}{3}x-\dfrac{2}{3}\\\\\\y\quad \ =\dfrac{1}{3}x-\dfrac{2}{3}+\dfrac{12}{3}\\\\\\\large\boxed{y\quad =\dfrac{1}{3}x+\dfrac{10}{3}}[/tex]
