The equation of the line is the vertical line x = 3.
<h3>The gradient of the line</h3>
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 = +∞
<h3>Equation of the line in point-slope form</h3>
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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