Hi,

the standard slope-intercept form for an equation of a line y = mx + b  

where m is the slope and b the y-intercept.

Line parallel to the following  

 x +6y=5   Solving for y to put into the slope-intercept form

y = -x/6 + 5/6  m = (-1/6)

New line parallel to this line has the same slope

y = -x/6 + b  Using ordered pair Pt(2,4) to solve for b

4 = -2/6 + b

4 + 1/3 =  13/3 = b

y = -x/6 + 13/3



 

Answer by jessica43(140)   (Show Source): You can put this solution on YOUR website!
 For two lines to be parallel, they must have the same slopes.  So first we need to rewrite the given line in the formula of y = mx + b:

x + 6y = 5

6y = 5 - x

y = 5/6 - (1/6)x

Now that it is written in the correct formula, we can see that m = -1/6, which is the slope of this line. So our line must have this same slope.

Now we need to plug in what we know (the slope and the point (2,4)) into the y = mx + b formula:

y = mx + b

4 = (-1/6)(2) + b

Now solve for b:

4 = (-1/6)(2) + b

4 = (-2/6) + b

26/6 = b

So your equation of the line is y = (-1/6)x + 26/6 

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