Hi,

Note:  x-5y =1  is 

the standard slope-intercept form for an equation of a line is 

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



write an equation of the line containing P(-1,-6) and parallel to 

New Line:  Slopes are the same

   |using P(-1,-6) to solve for b

 

  -6 = -1/5 + b

 -30/5 + 1/5 = b

 

In standard form:

 x - 5y = 29



 

Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
 the line you need to be parallel to is in the equation of x - 5y = 1

you need to find the slope of this line.

the easiest way is to convert the equation to slope intercept form.

slope intercept form is y = mx + b

m is the slope and b is the y-intercept

start with:

x - 5y = 1

add 5y to both sides of this equation to get:

x = 1 + 5y

subtract 1 from both sides of this equation to get:

x - 1 = 5y

commute this equation to get (flip sides):

5y = x - 1

divide both sides of this equation by 5 to get:

y = (x-1)/5

simplify this equation to get:

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

the slope is equal to (1/5).

the line you create needs to be parallel to this line.

the slope of the line you create needs to be the same as the slope of this line because parallel lines have the same slope.

the slope intercept form of your line will be y = mx + b where m is the slope and b is the y-intercept.

m is replaced with (1/5).

the equation of your new line will be y = (1/5)x + b

you now need to find b.

b can be found in a couple of ways.





one of those ways is to use the slope intercept form of the equation and replace y with the y-coordinate of the point the new line will be going through and replace x with the x-coordinate of the point the new line will be going through and then solving for b.

we'll do it that way.





start with y = (1/5)x + b

the point your new line will be going through is (x,y) = (-1,-6).

replace y with -6 and x with -1 to get:

-6 = (1/5)(-1) + b

simplify to get:

-6 = -1/5 + b

add 1/5 to both sides of the equation to get:

-6 + 1/5 = b

commute this equation to get:

b = -6 + 1/5

convert the equation to improper fractions to get:

b = -30/5 + 1/5

simplify to get:

b = -29/5

the equation of the line parallel to the original line will be:

y = (1/5) - 29/5





you can also solve for the equation by using the point slope form of the equation of a straight line.

we'll do it that way this time.





your slope is (1/5)

the point slope form of the equation of a straight line is y - y1 = m * (x - x1).

your slope is (1/5).

your point is (-1,-6)

your point is represented by (x1,y1), so (x1,y1) = -1,-6

start with:

y - y1 = m * (x - x1)

replace m with (1/5) to get:

y - y1 = (1/5) * (x - x1)

replace y1 with -6 and x1 with -1 to get:

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

simplify to get:

y + 6 = (1/5) * (x + 1)

simplify to get:

y + 6 = (1/5) * x + (1/5) * 1

simplify further to get:

y + 6 = (1/5) * x + 1/5

subtract 6 from both sides of this equation to get:

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

multiply 6 by 5/5 to get 6 = 30/5

replace 6 with 30/5 to get:

y = (1/5) * x + 1/5 - 30/5

simplify to get:

y = (1/5) * x - 29/5

that's your equation.

y = (1/5)x - 29/5





you get the same equation using either method.





your solution is:





y = (1/5)x - 29/5





the graph of the original equation and your new equation are shown below.





the equation used are:





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

original equation after converting to slope intercept form.





y = (1/5)x - 29/5 

new equation parallel to original equation going through the point (-1,-6).











you can see that the lines are parallel.





the y-intercept of the original equation of y = (1/5)x - 1/5 is equal to 1/5 which has a decimal equivalent of .2, as shown on the graph.





the y-intercept of the new equation of y = (1/5)x - 29/5 is equal to -29/5 which has a decimal equivalent of -5.8 as shown on the graph.







 

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