Question 119191
{{{3*x-5*y=9}}} Start with the given equation


Let's find the x-intercept


To find the x-intercept, let y=0 and solve for x:

{{{3*x-5*(0)=9}}} Plug in {{{y=0}}}


{{{3*x=9}}} Simplify


{{{x=9/3}}} Divide both sides by 3



{{{x=3}}} Reduce




So the x-intercept is *[Tex \Large \left(3,0\right)] (note: the x-intercept will always have a y-coordinate equal to zero)




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{{{3*x-5*y=9}}} Start with the given equation


Now let's find the y-intercept


To find the y-intercept, let x=0 and solve for y:

{{{3*(0)-5*y=9}}} Plug in {{{x=0}}}


{{{-5*y=9}}} Simplify


{{{x=9/-5}}} Divide both sides by -5




{{{y=-9/5}}} Reduce




So the y-intercept is *[Tex \Large \left(0,-\frac{9}{5}\right)] (note: the y-intercept will always have a x-coordinate equal to zero)


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So we have these intercepts:

x-intercept: *[Tex \Large \left(3,0\right)]


y-intercept: *[Tex \Large \left(0,-\frac{9}{5}\right)]