What is the equation of the line with slope # m= 1/3 # that passes through # (-7/15,-5/24) #?

2 Answers
Feb 14, 2016

#y=x/3-19/360#

Explanation:

#y=mx+c#

#-5/24=1/3 * (-7/15) + c#

#c=-5/24+1/3*7/15#

#c=-19/360#

-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-
Let the desired equation be

#y=mx+c#
To find out #c#, insert values of the #m, x and y# coordinates from the given point.
#-5/24=(1/3)*(-7/15)+c#

#=>c=-5/24+1/3*7/15#

#=>c=-5/24+7/45#
#=>c=(-5*15+7*8)/360#
#=>c=(-75+56)/360#
#=>c=-19/360#

Feb 14, 2016

#y=1/3x-19/360#

Explanation:

The first answer is correct, but I would like to provide an alternative solution using the point-slope form.

Point-slope form:

Given a point #(x_0,y_0)# and a slope #m#, the equation of the line is:

#" "y-y_0=m(x-x_0)#

You just have to substitute everything.

Solution

#[1]" "y-y_0=m(x-x_0)#

#[2]" "y+5/24=1/3(x+7/15)#

#[3]" "y+5/24=1/3x+7/45#

#[4]" "y=1/3x+7/45-5/24#

#[5]" "y=1/3x+7/45-5/24#

#[6]" "y=1/3x+(56-75)/360#

#[7]" "color(blue)(y=1/3x-19/360)#