Answer
Lines $a$ and $b$ have slopes of $-\frac{1}{4}$, so they are parallel.
Work Step by Step
Line $a:$
Let $(x_1,y_1)=(0,4)$ and $(x_2,y_2)=(4,3)$
Slope
$\Rightarrow m_a=\frac{y_2-y_1}{x_2-x_1}$
Substitute all the values.
$\Rightarrow m_a=\frac{3-4}{4-0}$
Simplify.
$\Rightarrow m_a=-\frac{1}{4}$
Line $b:$
Let $(x_1,y_1)=(0,1)$ and $(x_2,y_2)=(4,0)$
Slope
$\Rightarrow m_b=\frac{y_2-y_1}{x_2-x_1}$
Substitute all the values.
$\Rightarrow m_b=\frac{0-1}{4-0}$
Simplify.
$\Rightarrow m_b=-\frac{1}{4}$
Line $c:$
Let $(x_1,y_1)=(2,0)$ and $(x_2,y_2)=(4,4)$
Slope
$\Rightarrow m_c=\frac{y_2-y_1}{x_2-x_1}$
Substitute all the values.
$\Rightarrow m_c=\frac{4-0}{4-2}$
Simplify.
$\Rightarrow m_c=\frac{4}{2}$
$\Rightarrow m_c=2$
Lines $a$ and $b$ have slopes of $-\frac{1}{4}$, so they are parallel.
