What is the slope of a line that is perpendicular to the line shown.Answer options: 2/3, -3, 3, -1/3

Answer:3Step-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:(0,3) and (3,2)Therefore, the slope of the line shown is[tex]m=\frac{2-3}{3-0}=-\frac{1}{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{1}{3}[/tex], we find that a line perpendicular to the line shown should have a slope of[tex]m_2 = -\frac{1}{-1/3}=3[/tex]