Answer:
The slope of line r is -3/4
Step-by-step explanation:
First, let's find the slope of line q. We can find the slope by finding the change in y over change in x.
[tex]\displaystyle{m=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]
Therefore, substitute in:
[tex]\displaystyle{m=\dfrac{8-4}{6-3}}\\\\\displaystyle{m=\dfrac{4}{3}}[/tex]
Therefore, the slope of line q is 4/3. Since we want to find the slope of line r and we know by the given that line r is perpendicular to line q. By the definition of perpendicular line is [tex]\displaystyle{m_1m_2=-1}[/tex].
Let [tex]m_1[/tex] be slope of the line q which is 4/3. Therefore, substitute in and solve for [tex]m_2[/tex] (slope of line r)
[tex]\displaystyle{\dfrac{4}{3}m_2=-1}\\\\\displaystyle{4m_2=-3}\\\\\displaystyle{m_2=-\dfrac{3}{4}}[/tex]
Therefore, the slope of line r is -3/4
