Question

Please assist me with these problems​

Answer 1

Part (a)

Answer: y1 and y3 are perpendicular

This is because the two slopes 2 and -1/2 multiply to -1. Perpendicular slopes multiply to -1 assuming neither line is vertical or horizontal.

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Part (b)

Graph each line to see where they cross. The three points of intersection are

(0,4)

(2,-2)

(4,2)

The order of the points doesn't matter.

You could also form three systems of equations pairing up the equations, and solving each system. That way you can find the points of intersection. Graphing may be a better and faster route in my opinion. See the diagram below.

Answer 2

Answer: c) y₁ and y₃ are perpendicular

Explanation:

Perpendicular (⊥) means the lines have opposite (change the sign) and reciprocal (flip the fraction) slopes.

y₁ = 2x - 6

↓

m= 2

m⊥= -(1/2)

y₂ = -3x + 4

↓

m= -3

m⊥= +(1/3)

y₃ = -(1/2)x + 4

↓

m= -(1/2)

m⊥= +2

y₁ and y₃ have opposite reciprocal slopes so they are perpendicular to each other.