Question 926148

<h4>x-intercept</h4>

To find the x-intercept, plug in {{{y=0}}} and solve for x



{{{x-5y=-4}}} Start with the given equation.



{{{x-5(0)=-4}}} Plug in {{{y=0}}}.



{{{x-0=-4}}} Multiply {{{-5}}} and 0 to get 0.



{{{x=-4}}} Simplify.



So the x-intercept is *[Tex \LARGE \left(-4,0\right)].



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<h4>y-intercept</h4>

To find the y-intercept, plug in {{{x=0}}} and solve for y



{{{x-5y=-4}}} Start with the given equation.



{{{0-5y=-4}}} Plug in {{{x=0}}}.



{{{-5y=-4}}} Simplify.



{{{y=(-4)/(-5)}}} Divide both sides by {{{-5}}} to isolate {{{y}}}.



{{{y=4/5}}} Reduce.



So the y-intercept is *[Tex \LARGE \left(0,\frac{4}{5}\right)].



Now let's plot the points *[Tex \LARGE \left(-4,0\right)] and *[Tex \LARGE \left(0,\frac{4}{5}\right)] which are the x and y intercepts respectively.



{{{drawing(500, 500, -10,10,-10,10,
grid(0),
graph(500, 500, -10,10,-10,10,0)
circle(-4,0,0.03),circle(-4,0,0.05),circle(-4,0,0.08),circle(-4,0,0.10),circle(-4,0,0.12),
circle(0,4/5,0.03),circle(0,4/5,0.05),circle(0,4/5,0.08),circle(0,4/5,0.10),circle(0,4/5,0.12)
)}}}



Now draw a straight line through the plotted points to graph {{{x-5y=-4}}}.



{{{ drawing(500, 500, -10,10,-10,10,
grid(0),
graph(500, 500, -10,10,-10,10,0,(-4-x)/(-5)),
circle(-4,0,0.03),circle(-4,0,0.05),circle(-4,0,0.08),circle(-4,0,0.10),circle(-4,0,0.12),
circle(0,4/5,0.03),circle(0,4/5,0.05),circle(0,4/5,0.08),circle(0,4/5,0.10),circle(0,4/5,0.12)
)}}} Graph of {{{x-5y=-4}}}
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