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. (-2, 3) and (0, 2)
Step 1: [tex]m=\dfrac{3-2}{-2-0}\quad =\dfrac{1}{-2}\quad =-\dfrac{1}{2}[/tex]
Step 2: [tex]y-2=-\dfrac{1}{2}(x-0)[/tex]
[tex]y-2=-\dfrac{1}{2}x[/tex]
[tex]\large\boxed{y=-\dfrac{1}{2}x+2}[/tex]
2. (2, 3) and (-3, 0)
Step 1: [tex]m=\dfrac{3-0}{2-(-3)}\quad =\dfrac{3-0}{2+3}\quad =\dfrac{3}{5}[/tex]
Step 2: [tex]y-0=\dfrac{3}{5}(x-(-3))[/tex]
[tex]y=\dfrac{3}{5}(x+3)[/tex]
[tex]\large\boxed{y=\dfrac{3}{5}x+\dfrac{9}{5}}[/tex]
3. (-4, 4) and (4, 5)
Step 1: [tex]m=\dfrac{4-5}{-4-4}\quad =\dfrac{-1}{-8}\quad =\dfrac{1}{8}[/tex]
Step 2: [tex]y-4=\dfrac{1}{8}(x-(-4))[/tex]
[tex]y-4=\dfrac{1}{8}(x+4)[/tex]
[tex]y-4=\dfrac{1}{8}x+\dfrac{1}{2}[/tex]
[tex]\large\boxed{y=\dfrac{1}{8}x+\dfrac{9}{2}}[/tex]
4. (5, 3) and (-1, 5)
Step 1: [tex]m=\dfrac{3-5}{5-(-1)}\quad =\dfrac{3-5}{5+1}\quad =\dfrac{-2}{6}\quad =-\dfrac{1}{3}[/tex]
Step 2: [tex]y-3=-\dfrac{1}{3}(x-5)[/tex]
[tex]y-3=-\dfrac{1}{3}x+\dfrac{5}{3}[/tex]
[tex]\large\boxed{y=-\dfrac{1}{3}x+\dfrac{14}{3}}[/tex]
5. (-3, 3) and (0, -1)
Step 1: [tex]m=\dfrac{3-(-1)}{-3-0}\quad =\dfrac{3+1}{-3-0}\quad =\dfrac{4}{-3}\quad =-\dfrac{4}{3}[/tex]
Step 2: [tex]y-3=-\dfrac{4}{3}(x-(-3))[/tex]
[tex]y-3=-\dfrac{4}{3}(x+3)[/tex]
[tex]y-3=-\dfrac{4}{3}x-4[/tex]
[tex]\large\boxed{y=-\dfrac{4}{3}x-1}[/tex]
