Question

`\huge\boxed{Write\;equations\;for\;the\;following...}\\\\1...\;\;(0, -2) & (3,0)\\2...\;\;(0, -3) & (-4, -5)\\3...\;\;(-3,-4) & (4,3)\\\\\\\boxed{Please\;show\;work!}`

Answer 1

1. y = -2/3x + 2

2. y = 2/4x + -3

3. y = 1x -1

Answer 2

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

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

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

`y=(2)/(3)(x-3)`

`\large\boxed{y=(2)/(3)x-2}`

2. (0, -3) and (-4, -5)

Step 1:
`m=(-3-(-5))/(0-(-4))\quad =(-3+5)/(0+4)\quad =(2)/(4)\quad =(1)/(2)`

Step 2:
`y-(-3)=(1)/(2)(x-0)`

`y+3=(1)/(2)x`

`\large\boxed{y=(1)/(2)x-3}`

3. (0, -3) and (-4, -5)

Step 1:
`m=(-4-3)/(-3-4)\quad =(-7)/(-7)\quad =1`

Step 2:
`y-3=1}(x-4)`

`y-3=x-4`

`\large\boxed{y=x-1}`