Question

`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)`

Answer 1

Answer: see below

Explanation:

Step 1: Find the slope (m) using the formula:
`m=(y_2-y_1)/(x_2-x_1)`

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:
`m=(3-2)/(-2-0)\quad =(1)/(-2)\quad =-(1)/(2)`

Step 2:
`y-2=-(1)/(2)(x-0)`

`y-2=-(1)/(2)x`

`\large\boxed{y=-(1)/(2)x+2}`

2. (2, 3) and (-3, 0)

Step 1:
`m=(3-0)/(2-(-3))\quad =(3-0)/(2+3)\quad =(3)/(5)`

Step 2:
`y-0=(3)/(5)(x-(-3))`

`y=(3)/(5)(x+3)`

`\large\boxed{y=(3)/(5)x+(9)/(5)}`

3. (-4, 4) and (4, 5)

Step 1:
`m=(4-5)/(-4-4)\quad =(-1)/(-8)\quad =(1)/(8)`

Step 2:
`y-4=(1)/(8)(x-(-4))`

`y-4=(1)/(8)(x+4)`

`y-4=(1)/(8)x+(1)/(2)`

`\large\boxed{y=(1)/(8)x+(9)/(2)}`

4. (5, 3) and (-1, 5)

Step 1:
`m=(3-5)/(5-(-1))\quad =(3-5)/(5+1)\quad =(-2)/(6)\quad =-(1)/(3)`

Step 2:
`y-3=-(1)/(3)(x-5)`

`y-3=-(1)/(3)x+(5)/(3)`

`\large\boxed{y=-(1)/(3)x+(14)/(3)}`

5. (-3, 3) and (0, -1)

Step 1:
`m=(3-(-1))/(-3-0)\quad =(3+1)/(-3-0)\quad =(4)/(-3)\quad =-(4)/(3)`

Step 2:
`y-3=-(4)/(3)(x-(-3))`

`y-3=-(4)/(3)(x+3)`

`y-3=-(4)/(3)x-4`

`\large\boxed{y=-(4)/(3)x-1}`