How do you find the x and y intercept of #3x − 5y = −10#?

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Answer 1 · 2017-04-08T05:37:55

Isolate for each variable by subbing in #0# for the other. In this case, we get #(-10/3, 0)# as the #x#-intercept, and #(0, 2)# as the #y#-intercept.

To find the zeros, all we have to do is sub in one variable as #0# and isolate for the other.

Solving for #x#-intercept

This happens when the #y#-value is #0#, thus we sub in #0# as the #y#-value.

#3x - 5y = -10#

#3x - 5(0) = -10#

Now we solve for #x#.

#3x - 0 = -10#

#3x = -10#

#x = -10/3#

The #x#-intercept is #(-10/3, 0)#.

Solving for #y#-intercept

This happens when the #x#-value is #0#, thus we sub in #0# as the #x#-value.

#3x - 5y = -10#

#3(0) - 5y= -10#

Now we solve for #y#.

#-5y= -10#

#y = (-10)/-5#

#y = 2#

The #y#-intercept is #(0, 2)#.

We can graph the equation to check our work.

graph{3x - 5y = -10 [-10, 10, -5, 5]}

As we can see, our intercepts are correct.

Hope this helps :)