What is the equation of the line that passes through the two points (-2,3) and (2,-3)?

the point-slope form of the equation:    y + 3 = -³/₂(x - 2)    

the slope-intercept form of the equation:   y = -³/₂x

standard form of the equation:        3x + 2y = 0

Step-by-step explanation:

(-2, 3)    ⇒   x₁ = -2,  y₁ = 3

(2, -3)    ⇒   x₂ = 2,  y₂ = -3

So the slope:

The point-slope form of equation is : y - y₀ = m(x - x₀), where (x₀, y₀) is any point the line passes through.

(2, -3)    ⇒   x₀ = 2,  y₀ = -3

Therefore:

y + 3 = -³/₂(x - 2)       ←  the point-slope form of the equation

y + 3 = -³/₂x + 3

y = -³/₂x                    ←  the slope-intercept form of the equation (b=0)

y + ³/₂x = 0

3x + 2y = 0               ←  standard form of the equation