How do you write an equation in slope-intercept form for a line that is parallel to the given line y = 1/3x + 5 and passes through the given point(0,-5)?

1 Answer
Jul 3, 2015

Answer:

#y=1/3x-5#

Explanation:

As you might know, lines that are parallel have the same value at #x#, in this case #1/3#. This is because this represents the slope of the line, and same slope means parallel lines.
To get the full equation, there is a formula, but there's also a way if you don't know the formula. Let's do it without the formula first:

Without the formula
Let's write down what we know of our function at the moment:
#y=1/3x+c#
All we need to know is #c#. Since we know one of the points, we can just replace the #x# and #y# value and solve for #c#:
#-5=1/3*0+c#
#c=-5#
It's that easy! The equation is thus:
#y=1/3x-5#

With the formula
The formula to find the equation of a line through a given point and with a given slope is:

#y-y1=m(x-x1)#
where #y1# is the #y#-value of your point, #x1# the #x#-value and #m# the slope.
In this case, it will be:
#y-(-5)=1/3(x-0)#
#y+5=1/3x#
#y=1/3x-5#