Question

Here are some equations of straight lines: y+2x = 8 2y+*x+1=0 2y+x=1 y=x-4 y=2(x-1) 2y = x-4 y + 2x +2 = 0 y = x+2 y = 4-X 2y = 4-x 1. Which four lines form the four sides of a rectangle? Use the space on the back to show all work. Then, explain your reasoning carefully in the space below. 2. Graph the lines in the coordinate grid below and label each equation.

Answer 1

1) We know that a rectangle has 2 pairs of perpendicular sides. So the key point here is to find 2 pairs, i.e. 4 parallel lines. To have perpendicular sides we must have one line whose slope is reciprocal and opposite to th other Enlisting them we have:

• y+2x=8 ⇒y=-2x+8 m= -2

,

• 2y=x-4 ⇒y=1/2x -2 m=1/2

,

• 2y +1/2x +1=0 ⇒ 2y = -1/2x-1 ⇒ y =-1/4x-1/2 m=-1/4

,

• y+2x+2=0 ⇒ y= -2x -2 ⇒m =-2

,

• 2y +x =1 ⇒y =-1/2x+1 m = -1/2

,

• y=1/2x+2 ⇒m=1/2

,

• y=x-4 ⇒m=1

,

• y=4-x ⇒ m=-1

,

• y=2(x-1) ⇒ y= 2x -2 ⇒ m= 2

,

• 2y=4-x ⇒y= 2-1/2x ⇒m=-1/2

Now let's gather those lines whose slope is perpendicular and set our rectangle. Let's pick the parallel ones.

Considering the base of the rectangle made by slope m=-2

y+2x=8

y+2x+2=0

And perpendicular lines whose slope is m=1/2

2y=x-4

y=1/2x+2

2) Now Let's graph the lines in the coordinate grid, labeling them:

y+2x=8 (Red)

y+2x+2=0 (Light blue)

2y=x-4 (purple)

y=1/2x+2 (green)