Algebra 1
posted by Esther .
Write a equation of the line containing the given point and paralled to the given line (5,8);3x=5y+2

5y = 3 x  2
y = (3/5) x  2/5
so slope = 3/5
8 = (3/5)(5) + b
8 = 3 +b
b = 11
so
y = 3 x/5 + 11
or
5 y = 3x + 55 
Parallel to 3x = 5y + 2
through P(5,8)
Parallel lines have equal slopes
First, you need to put the given line in slopeintercept form, to find the slope.
Slopeintercept form,
y = mx + b
m = slope
b = yintercept
3x = 5y + 2
To put in slopeintercept form, solve for y.
3x = 5y + 2
5y = 3x  2
y = 3/5 x  2/5
So now you know that the slope m = 3/5.
y = 3/5 x  2/5
y = mx + b
Since parallel lines have the same slope, 3/5 will be the slope of your line through (5,8)
y = mx + b
y = 3/5 x + b
Now you need to use the point (5.8)
Since x = 5 and y = 8, put those value in your equation.
y = 3/5 x + b
8 = 3/5 (5) + b
All that's left is too solve for the b value.
8 = 3/5 (5) + b
8 = 15/5 + b
8 = 3 + b
b = 11
Now you have all you need for your parallel line
y = mx + b
slope m = 3/5
b = 11
y = 3/5 x + 11
Do you follow what I've done?
Good luck 
Thank you very much for your quick answer and for your time. However, I am still confused about how to get the top number on the left. For instance, the 11, or 55. What do you multiply, add, or divide?
Can you please use this one to show me step by step how you work out this problem? (8,6);2x=3y+4 I can get the first part, however, I can't figure how to work the last part of the problem. I really do appreciate your help, thank you.