How do you find the x and y intercepts for #f(x) = -3x-2#?

1 Answer
Aug 11, 2016

Answer:

y-intercept: #-2#

x-intercept: #-2/3#

Explanation:

Note that #f(x)# is equivalent to #y#.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The y-intercept is the value on the Y-axis where the function crosses the Y-axis. Since the Y-axis is the collection of points where #x=0#, it follows that the y-intercept is the value of the function when #x=0#.

Evaluating #f(x)=-3x-2# when #x=0#:
#color(white)("XXX")f(0)=-3(0)-2=-2#
So the y-intercept is at #(-2)#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Similarly, the x-intercept is the value of #x# when #y=0# (or equivalently when #f(x)=0#

Evaluating #f(x)=-3x-2# when #f(x)=0#
#color(white)("XXX")0=-3x-2#

#color(white)("XXX")rarr -3x=2#

#color(white)("XXX")rarr x=-2/3#
So the x-intercept is at #(-2/3)#

===========================================================