What are the intercepts of #-6y-2x=5#?

2 Answers
Dec 15, 2015

Answer:

#-2.5# or #-5/2#

Explanation:

Solve the equation for y:
#-6y - 2x = 5#
#-6y = 5-2x#
#y=((5-2x)/-6)#
Set the equation equal to zero in order to find the y values that are 0 which are the intercepts
#0 = ((5-2x)/-6)#
In order to get a fraction equal to 0, only the numerator needs to equal 0 so we can ignore the denominator
#0=-5-2x#
#5= -2x#
#5/-2 = x#
Intercept at #(-5/2,0)#

Dec 16, 2015

Finding the X-intercept:

Plug #0# in for #y#.

What this does, in effect, is causes the #-6y# term to disappear.

#color(red)(cancel(color(black)(-6y)))-2x=5#

#-2x=5#

#x=-5/2#

Thus, if #x=-5/2# and #y=0#, the point of the #x#-intercept is #(-5/2,0)#.

Finding the Y-intercept:

Similar to the previous example, plug in #0# for #x#. An easy way to think about this is just covering up #-2x# with your finger.

#-6ycolor(red)(cancel(color(black)(-2x)))=5#

#y=-5/6#

Which gives us a #y#-intercept of #(0,-5/6)#.

A graph of the line can help to confirm your answers:

graph{-(2x+5)/6 [-10, 10, -5, 5]}

The point where the line crosses the #x#-axis (the #x#-intercept) is #(-2.5,0)#, which equals #(-5/2,0)#.

The #y#-intercept on the graph is #(0,-0.833)#, which is equivalent to #(0,-5/6)#.