What is the slope of a line that is perpendicular to the line shown.Answer options: 2/3, 3/4, -3/4, -4/3.

Answer:3/4Step-by-step explanation:First of all, we need to calculate the slope of the line shown. This can be computed as:[tex]m=\frac{\Delta y}{\Delta x}[/tex]where[tex]\Delta y = y_2-y_1[/tex] is the increment along the y-direction[tex]\Delta x = x_2 - x_1[/tex] is the increment along the x-directionWe can choose the following two points to calculate the slope of the line shown:(-3,2) and (0,-2)And so, the slope of the line shown is[tex]m=\frac{-2-(2)}{0-(-3)}=-\frac{4}{3}[/tex]Two lines are said to be perpendicular if the slope of the first line is the negative reciprocal of the slope of the second line:[tex]m_2 = -\frac{1}{m_1}[/tex]Using [tex]m_1 = -\frac{4}{3}[/tex], we find that a line perpendicular to the line shown should have a slope of[tex]m_2 = -\frac{1}{-4/3}=3/4[/tex]