A model of Pythagorean Theorem is shown below. Based on the

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Answer:

1st pic answer:

Slope= -3

Parallel slope= -3

Perpendicular slope = 1/3

2nd pic answers:

1 and 2 are parallel

1 and 3 are perpendicular

2 and 3 are perpendicular

Step-by-step explanation:

To find the slope in your first equation (6x+2y=1) you need to get y alone so that your equation will be in slope-intercept form (y=mx+b).

6x+2y=1 Start by subtracting the 6x over to the other side.

-6x -6x

2y= -6x+1 Next divide by 2 to get y completely alone.

$\frac{2y}{2} =\frac{-6x}{2}+\frac{1}{2}$

y= -3x+1/2

So to answer the first part your slope is -3. Parallel slope would be the same as your regular slope. Perpendicular would be the opposite, so that means you have to flip it and change the sign.

-3 flipped is -1/3

if you change the sign it becomes positive giving you 1/3

Part 2

Your first step would be to get all the equations into the slope-intercept form (y=mx+b). The second one is already in the form so we only need to change 1 and 3.

3y=5x+2 To get y alone you need to divide everything by 3.

$\frac{3y}{3}=\frac{5x}{3} +\frac{2}{3}$

y=5/3x+2/3 Before we work on equation 3 we can go ahead and compare equations 1 and 2.

1: y= $\frac{5x}{3} +\frac{2}{3}$

2: y= $\frac{5x}{3} +7$ Since 1 and 2 have the same slope they would be parallel.

Now to change equation 3.

6x+10y=8 Start by subtracting the 6x over to the other side.

-6x -6x

10y=-6x+8 Now divide everything by 10 to get y alone.

$\frac{10y}{10}=\frac{-6x}{10} +\frac{8}{10}$

y=-6x/10+8/10 Now we need to simplify the fractions using common factors. I'm going to use 2 for both equations, so you take -6 and 10 both divided by 2, which gives you -3 and 5(-3x/5). Now do the same with the other fraction. 8 and 10 divided by 2 gives us 4 and 5 (4/5)

3: y= $\frac{-3x}{5}+\frac{4}{5}$