SOLUTION: pls help me to answer with solution ; what is the value of k so that the line x+(3k-2)y+10=0 and is parallel to the line x+5y+2=0

Question 888907: pls help me to answer with solution ; what is the value of k so that the line x+(3k-2)y+10=0 and is parallel to the line x+5y+2=0

Found 2 solutions by Fombitz, Theo:
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
Parallel lines have the same form, , where is distinct.
So then,

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
you want to to convert both equation into slope intercept form.

slope intercept form is y = mx + b

once in this form:

m = slope
b = y-intercept.

if the slope of both equation is the same and the y-intercept is different, then the lines are parallel.

start with x + 5y + 2 = 0
subtract x and subtract 2 from both sides of the equation to get:
5y = -x - 2
divide both sides of the equation by 5 to get:
y = -(1/5)*x - (2/5)

that's your first equation in slope intercept form.
the slope is -(1/5).

-(1/5) is the slope you want to get in your second equation in order to make the lines parallel to each other.

start with your second equation of x + (3k-2)y + 10 = 0
subtract 10 and subtract x from both sides of the equation to get:
(3k-2)y = -x - 10
divide both sides of the equation by (3k-2) to get:
y = -(1/(3k-2)*x - (10/(3k-2))

that's your second equation in slope intercept form.
the slope is -(1/(3k-2))

in order for the lines to be parallel, -(1/(3k-2)) must be equal to -(1/5).

set these two expressions equal to each other and solve for k.

-1/(3k-2) = -1/5

cross multiply to get:

-1*5 = -1*(3k-2)

divide both sides of this equation by (-1) to get:

5 = 3k-2

add 2 to both sides of this equation to get:

7 = 3k

divide both sides of this equation by 3 to get:

7/3 = k

that's your answer.

in order for the lines to be parallel, k has to be equal to 7/3.

to confirm, replace k with 7/3 in your original equation.

your original equation is x + (3k-2)y + 10 = 0
replace k with 7/3 to get:
x + (3*7/3-2)y + 10 = 0
simplify to get:
x + 5y + 10 = 0
subtract x and subtract 10 from both sides of the equation to get:
5y = -x - 10
divide both sides of the equation by 5 to get:
y = -(1/5)*x - (10/5)
simplify to get:
y = -(1/5)*x - 2

your first equation in slope intercept form is y = -(1/5)*x - (2/5)

your second equation in slope intercept form is y = -(1/5)*x - 2

the slopes are the same and the y-intercepts are different so the lines are parallel.

here's a graph of your two lines.

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