Answer:
The slope of FG is -1
Step-by-step explanation:
Given
Square EFGH
EF: [tex]x - y = 2[/tex]
Required
Determine the slope of FG
First, we calculate the slope of EF
[tex]x - y = 2[/tex]
Make y the subject
[tex]-y = 2 - x[/tex]
[tex]y = x -2[/tex]
The general equation has the form: [tex]y = mx + b[/tex]
Where
[tex]m = slope[/tex]
Compare [tex]y = mx + b[/tex] to [tex]y = x -2[/tex]
[tex]m = 1[/tex]
From the name of the square EFGH, we can conclude that EF and FG are perpendicular
The relationship between perpendicular lines is:
[tex]m_2 = -\frac{1}{m_1}[/tex]
Where
[tex]m_1 = m = 1[/tex] -- Slope of EF
and
m2 = slope of FG
Substitute 1 for m1 in [tex]m_2 = -\frac{1}{m_1}[/tex]
[tex]m_2 = -\frac{1}{1}[/tex]
[tex]m_2 = -1\\[/tex]
Hence, the slope of FG is -1
