Question

Write the equation of the line that passes through the points (3,-3) and (3,8). Put

Answer 1

The equation of the line is the vertical line x = 3.

The gradient of the line

The gradient of the line between two points (x₁, y₁) and (x₂, y₂) is m = (y₂ - y₁)/(x₂ - x₁).

Since the line passes through the points (3,-3) and (3,8),  

• (x₁, y₁) = (3,-3) and
• (x₂, y₂) = (3,8).

So, substituting the values of the variables into the equation, we have

m = (y₂ - y₁)/(x₂ - x₁).

m = (8 - (-3))/(3 - 3).

m = (8 + 3)/0

m = 11/0

m = +∞

Equation of the line in point-slope form

The equation of the line passing through the point (x₁, y₁) in point-slope form is given by

y - y₁ = m(x - x₁) where

• m = gradient = +∞ and
• (x₁, y₁) = (3, -3)

So, substituting the values of the variables into the equation, we have

y - y₁ = m(x - x₁)

y - (-3) = +∞(x - 3)

y + 3 = +∞(x - 3)

y + 3/+∞ = (x - 3)

0 = x - 3

x = 3

So, the equation of the line is the vertical line x = 3.

Learn more about equation of a line in point-slope form here:

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