How do you find the x and y intercepts for #5x -2y -6 =0#?

1 Answer

Answer:

x-intercept #(6/5, 0)#
y-intercept #(0,-3)#

Explanation:

The way to find intercepts is simple. All we need to do is first set one variable to zero. Let say we start with #y=0# then solve for the x-intercept. After which, set #x=0# then solve for y-intercept.

Let us do it.

#5x-2y-6=0#

Set #y=0# from the original equation

#5x-2y-6=0#

#5x-2(0)-6=0#

#5x-0-6=0#

#5x=6#

#(5x)/5=6/5#

#(cancel5x)/cancel5=6/5#

#x=6/5=1.2#

Now, Set #x=0# in the original equation #5x-2y-6=0#

#5(0)-2y-6=0#

#0-2y-6=0#
#-2y=6#

#(-2y)/(-2)=6/(-2)#

#(cancel(-2)y)/cancel(-2)=6/(-2)#

#y=6/(-2)#

#y=-3#

Kindly see the graph of #5x-2y-6=0#
We can see that the line intersects with the axes at #(6/5, 0) and #(0, -3)#

graph{5x-2y-6=0[-20,20,-10,10]}

God bless....I hope the explanation is useful.