Question

In the given graph,
Equation of line $AB:0.5x-0.25y=-0.25$
Equation of line $BC:y=5$
Rearrange the slopes of the lines in ascending order.

• A. $\text{Slope CD, slope BC, slope AB, slope DE}$
• B. $\text{Slope CD, slope BC, slope DE, slope AB}$
• C. $\text{Slope CD, slope DE, slope AB, slope BC}$
• D. $\text{Slope BC, slope CD, slope DE, slope AB}$

Answer 1

The correct option is B $\text{Slope CD, slope BC, slope DE, slope AB}$

Line AB:
$0.5x-0.25y=-0.25$
$\Rightarrow 0.5x+0.25=0.25y$
Dividing both sides by $0.25,$
$\Rightarrow 2x+1=y$
$\Rightarrow y=2x+1$
Comparing the equation with $y=mx+b,$
Slope $\left(m\right)=2$

Line BC:
The equation of line can be written as $y=0x+5.$
Slope $=0$

Line CD:
Slope$=\frac{5-(-5)}{3-8}=\frac{5+5}{-5}=\frac{10}{-5}=-2$

Line DE:
Slope $=\frac{-2-(-5)}{11-8}=\frac{-2+5}{3}=\frac{3}{3}=1$
Hence, $\text{slope CD, slope BC, slope DE, slope AB}$ is the correct sequence.