Question

(-2,0) and (3,4) slope=1/3 and (2,4) SOLVE EQUATIONS FOR THEM PLEASE

Answer 1

Answer:  $a)\quad y=\dfrac{4}{5}x+\dfrac{8}{5}$               $b)\quad y=\dfrac{1}{3}x+\dfrac{10}{3}$                

Step-by-step explanation:

Use the Slope formula:      $m=\dfrac{y_2-y_1}{x_2-x_1}$

and the Point-Slope formula:   y - y₁ = m(x - x₁)

a) (-2, 0) and (3, 4)

 $m=\dfrac{0-4}{-2-3}\quad =\dfrac{-4}{-5}\quad =\dfrac{4}{5}$

Let (x₁, y₁) = (-2, 0)      

y - y₁ = m(x - x₁)

$y-0=\dfrac{4}{5}\bigg(x-(-2)\bigg)\\\\\\y\quad =\dfrac{4}{5}\bigg(x+2\bigg)\\\\\\\large\boxed{y\quad =\dfrac{4}{5}x+\dfrac{8}{5}}$

b) m = 1/3     (x₁, y₁) = (2, 4)    

y - y₁ = m(x - x₁)

$y-4=\dfrac{1}{3}\bigg(x-2\bigg)\\\\\\y-4 =\dfrac{1}{3}x-\dfrac{2}{3}\\\\\\y\quad \ =\dfrac{1}{3}x-\dfrac{2}{3}+\dfrac{12}{3}\\\\\\\large\boxed{y\quad =\dfrac{1}{3}x+\dfrac{10}{3}}$