We want to find the slope of a line given that we know that the line passes through the points (6, 3) and (-6, -3).
We will find that the slope is: 1/2
A general line can be written as:
[tex]y = a\cdot x + b[/tex]
Where a is the slope and b is the y-intercept.
If the line passes through the points (x₁, y₁) and (x₂, y₂) then we can write the slope as:
[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
We know that our line passes through (6, 3) and (-6, -3), then the slope of our line will be:
[tex]a = \frac{-3 - 3}{-6 - 6} = \frac{-6}{-12}[/tex]
Now to simplify this, we know that:
-12 = 2×(-6)
Replacing that in the above equation we get:
[tex]a = \frac{-3 - 3}{-6 - 6} = \frac{-6}{-12} = \frac{-6}{2\cdot -6} = \frac{1}{2}[/tex]
Then the slope written as a simplified fraction is:
a = 1/2
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