Write an equation of the line containing the given point paralled to the given line (-8,6);2x=3y+4

Thank you

Esther, see your post below at 3:11pm that I answered. I gave you detailed instructions on how to do this almost exact problem.

You will never learn without attempting the problem yourself.

Post all your work if your are stuck.

(-8,6);2x=3y+4

I do understand the first part, but I still don't understand the second part. For instance,

3y=2x-4
y=(2/3)-4/3

the slope is 2/3

6=(2/3)(-8) this is where I'm getting stuck. I don't know if I should add, divide, or multiply these numbers to come up with the answer to the last part of the equation. I don't know what i'm doing wrong. I'm sorry, I really appreciate your patience and all your help.

(-8,6); 2x = 3y + 4

3y = 2x - 4
y =(2/3)x - 4/3
So, slope m = 2/3

Use y = mx + b and P(-8,6) to find the equation parallel

You know m = 2/3, so you have to find b.
y = 2/3 x + b
Put in x any y values and solve for b.
6 = 2/3 (-8) + b
See how my equation is different than yours? Where is the b in yours?

6 = 2/3 (-8) + b
6 = -16/3 + b
b = 6 + 16/3
b = 18/3 + 16/3
b = 34/3

y = 2/3 x + b
y = 2/3 x + 34/3
Check my arithmetic.

If it doesn't matter what form your new equation is in, then the above should be ok.

Hope this is clearer now.

OH! Thank God, I think i got it,now I know what I was doing wrong. It only took me a few days to get it,(really bad)but, I think I got it. Of course, it takes practice, but I think I'll be ok, I'm gonna practice more and I should be ok, thanks to you. Thank you very, very much for clearing that up for me. God Bless you.

If it's not too much asking, can you please explain the same way with this problem?

(6,7);9x+y=6. It looks similar to the first problem, except that this one doesn't have a minus sign. Thank you, again for all your help. If I make it through college, it is going to be because of wonderful, caring people like yourself.

Do you need a line parallel to 9x + y = 6?

Or?

I'm happy you understand!! Good work.

I'm sorry, I am so excited that I forgot to write what is needed for this problem.

Write an equation of the line containing the given point and perpendicular to the given line.
(6,7);9x+y=6

Thank you, again!

(6,7);9x+y=6

Put in y = mx + b form
9x + y = 6
y = -9x + 6

So slope m = -9

Perpendicular lines have slopes that are negative reciprocals of each other.
Meaning, m1 x m2 = -1

m1 = -9
-9 x m2 = -1
m2 = 1/9

So, the slope of the line will be 1/9
y = 1/9 x + b

To find b, P(6,7)
y = 1/9 x + b
7 = 1/9 (6) + b
7 = 6/9 + b
7 = 2/3 + b
b = 7 - 2/3
b = 21/3 - 2/3
b = 19/3

y = 1/9 x + b
y = 1/9 x + 19/3

Do you follow ?

Thank you for getting back to me. I seem to be having trouble figuring out the second part. For instance, I don't know how you went from 6/9 to 2/3. Also, I don't understand 7-2/3 or b= 21/3 - 2/3. I apologize, math is not my forte as you can see, i seem to learn much better step by step. I would really appreciate it if you can mention whether I should add, divide or multiply. However, since it is time consuming, if you can't, I will understand. Thank you for your patience and for all your help.

y = 1/9 x + b
7 = 1/9 (6) + b
7 = 6/9 + b
7 = 2/3 + b
b = 7 - 2/3
b = 21/3 - 2/3
b = 19/3

To find the equation of a line parallel to another line, we need to use the fact that parallel lines have the same slope.

Given the equation of the line, 2x = 3y + 4, we can rewrite it in slope-intercept form (y = mx + b) by isolating y:

2x - 4 = 3y

Divide both sides by 3 to get the coefficient of y to be 1:

(2/3)x - (4/3) = y

Now we know that the slope of this line is 2/3.

Since the line we are looking for is parallel to the given line, it will also have a slope of 2/3.

Next, we use the given point (-8, 6) to find the value of b, the y-intercept.

Substitute the coordinates into the slope-intercept form and solve for b:

6 = (2/3)(-8) + b
6 = -16/3 + b

To eliminate the fraction, we can convert 6 to a fraction by putting it over 1:

6/1 = -16/3 + b

To combine the fractions, we need a common denominator, which is 3:

18/3 = -16/3 + b

Simplify the equation:

18 = -16 + 3b

Combine like terms:

18 + 16 = 3b

34 = 3b

Divide both sides by 3 to solve for b:

34/3 = b

Now that we have the slope (m) and the y-intercept (b), we can write the equation of the line parallel to the given line:

y = (2/3)x + (34/3)

Therefore, the equation of the line parallel to the given line and passing through the point (-8, 6) is y = (2/3)x + (34/3).