1 answer

What is the equation of the line with slope # m= 17/3 # that passes through # (7/9,8/3) #?

Question:

What is the equation of the line with slope # m= 17/3 # that passes through # (7/9,8/3) #?

Answers

In slope point form: #(y-8/3) = (17/3)(x-7/9)#

In standard form: #153x-27y = 47#

Explanation:

The general slope-point form for a line with slope #m# through a point #(hatx,haty)# is
#color(white)("XXX")(y-haty) = m(x-hatx)#

For the given values this becomes:
#color(white)("XXX")(y-8/3)=(17/3)(x-7/9)#

To convert this to standard form we will need to do some simplification.

Begin clearing the denominators by multiplying both sides by #3#
#color(white)("XXX")3y-8 = 17(x-7/9)#
Continue clearing the denominators by multiplying both sides by #9#
#color(white)("XXX")27y-72 = 17(9x-7) = 153x-119#

Subtract #(153x)# from both sides
#color(white)("XXX")-153x + 27y -72 = -119#

Add #72# to both sides
#color(white)("XXX")-153x+27y = -47#

Multiply both sides by #(-1)#
#color(white)("XXX")153x-27y = 47#

.

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