Answer: see below
Step-by-step explanation:
Step 1: Find the slope (m) using the formula: [tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Step 2: Plug in the slope (m) and one of the points (x₁, y₁) into the Point-Slope formula. y - y₁ = m(x - x₁)
1. (0, -2) and (3, 0)
Step 1: [tex]m=\dfrac{-2-0}{0-3}\quad =\dfrac{-2}{-3}\quad =\dfrac{2}{3}[/tex]
Step 2: [tex]y-0=\dfrac{2}{3}(x-3)[/tex]
[tex]y=\dfrac{2}{3}(x-3)[/tex]
[tex]\large\boxed{y=\dfrac{2}{3}x-2}[/tex]
2. (0, -3) and (-4, -5)
Step 1: [tex]m=\dfrac{-3-(-5)}{0-(-4)}\quad =\dfrac{-3+5}{0+4}\quad =\dfrac{2}{4}\quad =\dfrac{1}{2}[/tex]
Step 2: [tex]y-(-3)=\dfrac{1}{2}(x-0)[/tex]
[tex]y+3=\dfrac{1}{2}x[/tex]
[tex]\large\boxed{y=\dfrac{1}{2}x-3}[/tex]
3. (0, -3) and (-4, -5)
Step 1: [tex]m=\dfrac{-4-3}{-3-4}\quad =\dfrac{-7}{-7}\quad =1[/tex]
Step 2: [tex]y-3=1}(x-4)[/tex]
[tex]y-3=x-4[/tex]
[tex]\large\boxed{y=x-1}[/tex]
