Answer
$m_{1}=-2$
$m_{2}=\dfrac{1}{2}$
$m_{3}=3$
$m_{4}=-\dfrac{1}{4}$
Work Step by Step
Refer to the attached image below for the graph. For every line, identify two points through which it passes and use the formula $m=\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}$ to obtain its slope.
$l_{1}$
It can be seen from the figure that the line $l_{1}$ passes through the points $(-2,4)$ and the origin, $(0,0)$. Find its slope:
$m=\dfrac{4-0}{-2-0}=\dfrac{4}{-2}=-2$
$l_{2}$
It can be seen from the figure that the line $l_{2}$ passes through the points $(0,2)$ and $(2,3)$. Find its slope:
$m=\dfrac{3-2}{2-0}=\dfrac{1}{2}$
$l_{3}$
It can be seen from the figure that the line $l_{3}$ passes through the points $(4,4)$ and $(3,1)$. Find its slope:
$m=\dfrac{1-4}{3-4}=\dfrac{-3}{-1}=3$
$l_{4}$
It can be seen from the figure that the line $l_{4}$ passes through the points $(-2,-1)$ and $(2,-2)$. Find its slope:
$m=\dfrac{-2+1}{2+2}=\dfrac{-1}{4}=-\dfrac{1}{4}$
