Answer:
The slope of the line perpendicular to the graphed line is 2.
Step-by-step explanation:
The Slope of a Line
Suppose we know the line passes through points A(x1,y1) and B(x2,y2). The slope can be calculated with the equation:
[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]
The graphed line passes through two visible points (0,4) and (8,0). Thus, its slope is:
[tex]\displaystyle m=\frac{0-4}{8-0}[/tex]
[tex]\displaystyle m=\frac{-4}{8}[/tex]
Simplifying:
[tex]\displaystyle m=-\frac{1}{2}[/tex]
Two lines of slopes m1 and m2 are perpendicular is:
[tex]m_1.m_2=-1[/tex]
Suposse the given line has slope [tex]m_1=-\frac{1}{2}[/tex]. To find m2, we solve the above equation:
[tex]\displaystyle m_2=-\frac{1}{m_1}[/tex]
Substituting:
[tex]\displaystyle m_2=-\frac{1}{-\frac{1}{2}}[/tex]
Operating
[tex]m_2=2[/tex]
The slope of the line perpendicular to the graphed line is 2.
