Question 536611


<h4>x-intercept</h4>

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



{{{4x-7y=-28}}} Start with the given equation.



{{{4x-7(0)=-28}}} Plug in {{{y=0}}}.



{{{4x-0=-28}}} Multiply {{{-7}}} and 0 to get 0.



{{{4x=-28}}} Simplify.



{{{x=(-28)/(4)}}} Divide both sides by {{{4}}} 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



{{{4x-7y=-28}}} Start with the given equation.



{{{4(0)-7y=-28}}} Plug in {{{x=0}}}.



{{{0-7y=-28}}} Multiply {{{4}}} and 0 to get 0.



{{{-7y=-28}}} Simplify.



{{{y=(-28)/(-7)}}} Divide both sides by {{{-7}}} to isolate {{{y}}}.



{{{y=4}}} Reduce.



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



Now let's plot the points *[Tex \LARGE \left(-7,0\right)] and *[Tex \LARGE \left(0,4\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(0,4,0.03),circle(0,4,0.05),circle(0,4,0.08),circle(0,4,0.10),circle(0,4,0.12)
)}}}



Now draw a straight line through the plotted points to graph {{{4x-7y=-28}}}.



{{{ drawing(500, 500, -10,10,-10,10,
grid(0),
graph(500, 500, -10,10,-10,10,(-28-4x)/(-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(0,4,0.03),circle(0,4,0.05),circle(0,4,0.08),circle(0,4,0.10),circle(0,4,0.12)
)}}} Graph of {{{4x-7y=-28}}}



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