<PRE><B>Question 189703</B>

&lt;h4&gt;x-intercept&lt;/h4&gt;

To find the x-intercept, plug in {{{y=0}}} and solve for x



{{{2x-5y=10}}} Start with the given equation.



{{{2x-5(0)=10}}} Plug in {{{y=0}}}.



{{{2x-0=10}}} Multiply {{{-5}}} and 0 to get 0.



{{{2x=10}}} Simplify.



{{{x=(10)/(2)}}} Divide both sides by {{{2}}} to isolate {{{x}}}.



{{{x=5}}} Reduce.



So the x-intercept is *[Tex \LARGE \left(5,0\right)].



------------------------------------------



&lt;h4&gt;y-intercept&lt;/h4&gt;

To find the y-intercept, plug in {{{x=0}}} and solve for y



{{{2x-5y=10}}} Start with the given equation.



{{{2(0)-5y=10}}} Plug in {{{x=0}}}.



{{{0-5y=10}}} Multiply {{{2}}} and 0 to get 0.



{{{-5y=10}}} Simplify.



{{{y=(10)/(-5)}}} Divide both sides by {{{-5}}} to isolate {{{y}}}.



{{{y=-2}}} Reduce.



So the y-intercept is *[Tex \LARGE \left(0,-2\right)].



Notice that if we graph the equation {{{2x-5y=10}}}, we can see that the graph has the x-intercept *[Tex \LARGE \left(5,0\right)] and the y-intercept *[Tex \LARGE \left(0,-2\right)]



{{{ drawing(500, 500, -7, 7, -7, 7,
grid(0),
graph(500, 500, -7, 7, -7, 7,(10-2x)/(-5))
)}}} Graph of {{{2x-5y=10}}}
</PRE>