How do you find slope, point slope, slope intercept, standard form, domain and range of a line for Line D (3, -7) (9,-3)?

1 Answer
Binayaka C.
Jan 24, 2018

Slope is #2/3# , point slope form is #y+7=2/3(x-3)#,
slope-intercept form is #y= 2/3x-9.#, standard form is
#2x-3y=27#.Domain: # x in RR or (-oo,oo)#. Range: # y in RR or (-oo,oo) #

Explanation:

The slope of the line passing through #(3,-7) and (9,-3)# is

#m= (y_2-y_1)/(x_2-x_1)= (-3+7)/(9-3)=4/6=2/3#

Point slope form of the line is #y-y_1=m(x-x_1)# or

#y+7=2/3(x-3)#

Let the equation of the line in slope-intercept form be #y=mx+c#

or #y=2/3x+c# . The point (3,-7) will satisfy the equation . So,

# -7= 2/3*3+c or c= -7-2= -9#. Hence the equation of

the line in slope-intercept form is #y= 2/3x-9.#

The equation of the line in standard form is #3y=2x-27# or

#2x-3y=27#.

Domain of the line #y= 2/3x-9.# is any real value of #x#

Domain: # x in RR or (-oo,oo) #

Range of the line #y= 2/3x-9.# is any real value of #y#

Range: # y in RR or (-oo,oo) #

graph{2/3x-9 [-40, 40, -20, 20]}

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