[tex]Write\;equations\;for\;the\;following...\\\\1...(-2, 3) & (0, 2\\2...(2, 3) & (-3, 0)\\3...(-4, 4) & (4, 5)\\4...(5, 3) & (-1, 5)\\5...(-3, 3) & (0. -1)[/tex]

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]

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