What is the equation of the line with slope # m= -11/3 # that passes through # (13/15,-23/24) #?

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Answer 1 · 2016-03-15T18:16:31

#y=-11/3x+799/360#

Recall that the general equation of a line is:

#color(blue)(|bar(ul(color(white)(a/a)y=mx+bcolor(white)(a/a)|)))#

where:
#y=#y-coordinate
#m=#slope
#x=#x-coordinate
#b=#y-intercept

Determining the Equation
#1#. Start by substituting #color(orange)(m=-11/3)# into the formula.

#y=mx+b#

#y=color(orange)(-11/3)x+b#

#2#. Since you are also given the coordinate, #(color(purple)(13/15),color(teal)(-23/24))#, substitute it into the equation as well.

#color(teal)(-23/24)=color(orange)(-11/3)color(purple)((13/15))+b#

#3#. Solve for the unknown value of the variable, #b#.

#-23/24=-143/45+b#

#b=799/360#

#4#. Rewrite the equation.

#color(green)(|bar(ul(color(white)(a/a)y=-11/3x+799/360color(white)(a/a)|)))#