Question 94085


{{{5*x-8*y=16}}} Start with the given equation


Let's find the x-intercept


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

{{{5*x-8*(0)=16}}} Plug in {{{y=0}}}


{{{5*x=16}}} Simplify


{{{x=16/5}}} Divide both sides by 5




So the x-intercept is ({{{16/5}}},0) (note: the x-intercept will always have a y-coordinate equal to zero)


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{{{5*x-8*y=16}}} Start with the given equation


Now let's find the x-intercept


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

{{{5*(0)-8*y=16}}} Plug in {{{x=0}}}


{{{8*y=16}}} Simplify


{{{x=16/-8}}} Divide both sides by -8




{{{y=-2}}} Reduce




So the y-intercept is (0,{{{-2}}}) (note: the y-intercept will always have a x-coordinate equal to zero)


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So we have these intercepts:

x-intercept: ({{{16/5}}},0)


y-intercept: (0,{{{-2}}})




Now plot the two points ({{{16/5}}},0) (which is the point (3.2 ,0) in decimal form)  and (0,{{{-2}}}) 


{{{drawing(500, 500, -5.2, 5.2, -4, 4,
graph(500, 500, -5.2, 5.2, -4, 4,0),
circle(3.2,0,0.0577777777777778),
circle(3.2,0,0.0877777777777778),

circle(0,-2,0.0577777777777778),
circle(0,-2,0.0877777777777778)


)}}}



Now draw a line through the two points to graph {{{5*x-8*y=16}}}

{{{drawing(500, 500, -5.2, 5.2, -4, 4,
graph(500, 500, -5.2, 5.2, -4, 4,(16-5*x)/-8),
circle(3.2,0,0.0577777777777778),
circle(3.2,0,0.0877777777777778),

circle(0,-2,0.0577777777777778),
circle(0,-2,0.0877777777777778)


)}}} graph of {{{5*x-8*y=16}}} through the points ({{{16/5}}},0) and (0,{{{-2}}})