Question 583707
To plot this graph, we just need two points. So let's find the x and y intercepts.


<h4>x-intercept</h4>

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



{{{2x-7y=14}}} Start with the given equation.



{{{2x-7(0)=14}}} Plug in {{{y=0}}}.



{{{2x-0=14}}} Multiply {{{-7}}} and 0 to get 0.



{{{2x=14}}} Simplify.



{{{x=(14)/(2)}}} Divide both sides by {{{2}}} to isolate {{{x}}}.



{{{x=7}}} Reduce.



So the x-intercept is *[Tex \LARGE \left(7,0\right)].



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<h4>y-intercept</h4>

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



{{{2x-7y=14}}} Start with the given equation.



{{{2(0)-7y=14}}} Plug in {{{x=0}}}.



{{{0-7y=14}}} Multiply {{{2}}} and 0 to get 0.



{{{-7y=14}}} Simplify.



{{{y=(14)/(-7)}}} Divide both sides by {{{-7}}} to isolate {{{y}}}.



{{{y=-2}}} Reduce.



So the y-intercept is *[Tex \LARGE \left(0,-2\right)].



Now let's plot the points *[Tex \LARGE \left(7,0\right)] and *[Tex \LARGE \left(0,-2\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(7,0,0.03),circle(7,0,0.05),circle(7,0,0.08),circle(7,0,0.10),circle(7,0,0.12),
circle(0,-2,0.03),circle(0,-2,0.05),circle(0,-2,0.08),circle(0,-2,0.10),circle(0,-2,0.12)
)}}}



Now draw a straight line through the plotted points to graph {{{2x-7y=14}}}.



{{{ drawing(500, 500, -10,10,-10,10,
grid(0),
graph(500, 500, -10,10,-10,10,(14-2x)/(-7)),
circle(7,0,0.03),circle(7,0,0.05),circle(7,0,0.08),circle(7,0,0.10),circle(7,0,0.12),
circle(0,-2,0.03),circle(0,-2,0.05),circle(0,-2,0.08),circle(0,-2,0.10),circle(0,-2,0.12)
)}}} Graph of {{{2x-7y=14}}}


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Jim