SOLUTION: Hi i really need help with my homework. I dont know how to do this problem. "Through point (3,1) with the same slope as line 2x-3y=1"

Algebra ->  Test -> SOLUTION: Hi i really need help with my homework. I dont know how to do this problem. "Through point (3,1) with the same slope as line 2x-3y=1"      Log On


   

Question 426456: Hi i really need help with my homework. I dont know how to do this problem.
"Through point (3,1) with the same slope as line 2x-3y=1"
Found 2 solutions by mananth, josmiceli:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
2x-3y=1
Find the slope of this line

-3y=-2x+1
Divide by -3
y=0.67x -0.33
Compare this equation with y=mx+b
slope m =0.67

The slope of a line parallel to the above line will be the same
The slope of the required line will be 0.67
m=0.67 ,point (3,1)
Find b by plugging the values of m & the point in
y=mx+b
1=2+b
b= -1
m= 0.67
Plug value of the slope and b
The required equation is y =0.67x-1

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
First, get the equation into the form
+y+=+m%2Ax+%2B+b+
In this form, m = slope
given:
+2x+-+3y+=+1+
Subtract 2x from both side
+-3y+=+-2x+%2B+1+
Divide both sides by -3
+y+=+%282%2F3%29%2Ax+-+1%2F3+
+m+=+2%2F3+
Any line parallel to this one will also have +m+=+2%2F3+
So far you have
+y+=+%282%2F3%29%2Ax+%2B+b+ for the new line
It goes through (3,1), so I can plug this x and y into equation
to get b
+1+=+%282%2F3%29%2A3+%2B+b+
+1+=+2+%2B+b+
+b+=+-1+
So, the equation is
y+=+%282%2F3%29%2Ax+-+1 answer
Check: Does it go through (3,1)?
+1+=+%282%2F3%29%2A3+-+1+
+1+=+2+-+1+
+1+=+1+
OK