Question

Are the following equations parallel,
perpendicular or neither?
y=-1/2+3 10x-5y=15

Answer 1

10x-5y=15
-5y = 15 - 10x
-5y = -10x + 15
5y = 10x - 15
y = 2x - 15

They are perpendicular as the negative reciprocal of 2 is -1/2

Answer 2

Answer:

The given equations are perpendicular as their slopes are negative reciprocals.

Step-by-step explanation:

Given equations:

$\begin{cases}y=-\dfrac{1}{2}x+3\\\\10x-5y=15\end{cases}$

Rearrange the second question to isolate y:

$\implies 10x-5y=15$

$\implies 10x-5y+5y=15+5y$

$\implies 10x=15+5y$

$\implies 10x-15=15+5y-15$

$\implies 10x-15=5y$

$\implies 5y= 10x-15$

$\implies \dfrac{5y}{5}=\dfrac{10x}{5}-\dfrac{15}{5}$

$\implies y=2x-3$

$\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\ y=mx+b \\\\where:\\ \phantom{ww} \bullet m is the slope. \\ \phantom{ww} \bullet b is the y -intercept.\\\end{minipage}}$

Therefore:

• The slope of the first equation is -¹/₂.
• The slope of the second equation is 2.

The slopes of parallel lines are the same.

The slopes of perpendicular lines are negative reciprocals.

The reciprocal of a number is 1 divided by the number.

Therefore, the negative reciprocal of 2 is -¹/₂.

The given equations are perpendicular as their slopes are negative reciprocals.