How do you find slope, point slope, slope intercept, standard form, domain and range of a line for Line G (6,0) (9,6)?

1 Answer
Mar 19, 2017

slope #=2#

point-slope equation: #y-0=2(x-6)#

slope-intercept equation: #y=2x-12#

standard form equation: #y-2x=-12#

domain: #(-oo, oo)#

range: #(-oo, oo)#

Explanation:

The slope, #m#, is:

#m= (y_2 - y_1)/(x_2 - x_1) = (6-0)/(9-6)#

This is the change in #y# between the two points over the change in #x# between the two points.

Once you have found the slope, pick one of the points and plug it into the point-slope formula:

#y-y_1=m(x-x_1)#

where #y_1# is the #y#-coordinate of one of the points and #x_1# is the #x#-coordinate of the same point and #m# is the slope. In this case, it is:

#y-0=2(x-6)#

To find the slope intercept form, just solve for #y#, but in this case, since I picked the point with a #y# of #0# and #y-0=y#, that is already done so the slope-intercept form is:

#y=2x-12#

The standard form formula is

#ax+by=c#

This can be found by just subtracting #2x# from both sides of the slope-intercept equation to get:

#y-2x=-12#

Lastly, the domain and range of any straight line are negative infinity to positive infinity.

Hope I helped out!