<PRE><B>Question 155615</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)].



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&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)]. So this verifies our answer.




{{{ drawing(500, 500, -3, 7, -5, 5,
grid(1),
graph(500, 500, -3, 7, -5, 5,(10-2x)/(5))
)}}} Graph of {{{2x+5y=10}}}</PRE>