Answer:
a) ¹/₂
b) -¹/₂
c) neither
Step-by-step explanation:
Slope-intercept form of a linear equation:
[tex]y=mx+b[/tex]
where:
- m is the slope
- b is the y-intercept
Given equations:
[tex]\begin{cases}-3x+6y=18\\-3x=6y+14 \end{cases}[/tex]
To find the slopes of the given equations, rearrange them to make y the subject then compare with the slope-intercept formula:
Equation 1
[tex]\begin{aligned}-3x+6y & = 18\\6y & = 3x + 18\\y & = \dfrac{3x+18}{6}\\\implies y & = \dfrac{1}{2}x+3\end{aligned}[/tex]
Therefore, the slope of Equation 1 is ¹/₂.
Equation 2
[tex]\begin{aligned}-3x & = 6y+14\\6y & = -3x-14\\y & = \dfrac{-3x-14}{6}\\\implies y& = -\dfrac{1}{2}x-\dfrac{14}{6}\end{aligned}[/tex]
Therefore, the slope of Equation 2 is -¹/₂.
Parallel slopes have the same slope.
Perpendicular slopes are at right angles to each other and therefore the product of their slopes is -1 (negative reciprocals of each other).
Therefore, the slopes of Equation 1 and Equation 2 are neither parallel or perpendicular.
