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.
[tex]\frac{2y}{2} =\frac{-6x}{2}+\frac{1}{2}[/tex]
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.
[tex]\frac{3y}{3}=\frac{5x}{3} +\frac{2}{3}[/tex]
y=5/3x+2/3 Before we work on equation 3 we can go ahead and compare equations 1 and 2.
1: y=[tex]\frac{5x}{3} +\frac{2}{3}[/tex]
2: y=[tex]\frac{5x}{3} +7[/tex] 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.
[tex]\frac{10y}{10}=\frac{-6x}{10} +\frac{8}{10}[/tex]
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=[tex]\frac{-3x}{5}+\frac{4}{5}[/tex]
2: y=[tex]\frac{5x}{3} +7[/tex]
1: y=[tex]\frac{5x}{3} +\frac{2}{3}[/tex]
Since three has an opposite slope of both 1 and 2 it would be perpendicular to both.
