Answer:
They are neither perpendicular nor parallel.
Step-by-step explanation:
Find the gradient of 2x + 6y = 42 by rearranging it in the form y = mx + c:
6y = -2x + 42
y = -(1/3)x + 7
The gradient is the co-efficient of x
Therefore the gradient is -(1/3)
The gradient of y = 2x - 1 is 2.
If they were parallel they would have the same gradient.
If they were perpendicular then the gradient of one would be the negative reciprocal of the other, e.g: if one was 2, the other would be -(1/2).
Neither of these are true, so they are neither perpendicular nor parallel.
The lines 3x+6y=42 and y=2x-1 are perpendicular
Two lines are parallel if they have equal slope
Two lines are perpendicular if the product of their slopes equals -1
The given lines are:
3x+6y=42 and y=2x-1
Rewrite each of the equations in the form y = mx + c
For line 3x + 6y = 42:
[tex]6y = -3x + 42\\\\y=\frac{-3}{6} x+\frac{42}{6}\\\\y=-0.5x+7[/tex]
The slope, m₁ = -0.5
For line y = 2x - 1
The slope, m₂ = 2
Since m₁ ≠ m₂, lines 3x+6y=42 and y=2x-1 are not parallel
m₁ m₂ = -0.5(2)
m₁ m₂ = -1
Since the product of the slopes equals -1, the lines 3x+6y=42 and y=2x-1 are perpendicular
Learn more here: https://brainly.com/question/20093063
