Question

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

Answer 1

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

Explanation:

`\bold{slope\, (m)=(change\ in\ Y)/(change\ in\ X)=(y_2-y_1)/(x_2-x_1)}`

(-2, 3) ⇒ x₁ = -2, y₁ = 3

(2, -3) ⇒ x₂ = 2, y₂ = -3

So the slope:

`\bold{m=(-3-3)/(2-(-2))=\frac{-6}4=-\frac32}`

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