Question 253665


<h4>x-intercept</h4>

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



{{{3x - 12y = -10}}} Start with the given equation.



{{{3x - 12(0) = -10}}} Plug in {{{y=0}}}.



{{{3x - 0 = -10}}} Multiply {{{12}}} and 0 to get 0.



{{{3x - 0 = -10}}} Simplify.



{{{3x=-10+0}}} Add {{{0}}} to both sides.



{{{3x=-10}}} Combine like terms on the right side.



{{{x=(-10)/(3)}}} Divide both sides by {{{3}}} to isolate {{{x}}}.



So the x-intercept is *[Tex \LARGE \left(-\frac{10}{3},0\right)].



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<h4>y-intercept</h4>

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



{{{3x - 12y = -10}}} Start with the given equation.



{{{3(0) - 12y = -10}}} Plug in {{{x=0}}}.



{{{0 - 12y = -10}}} Multiply {{{3}}} and 0 to get 0.



{{{ - 12y = -10}}} Simplify.



{{{y=(-10)/(-12)}}} Divide both sides by {{{-12}}} to isolate {{{y}}}.



{{{y=5/6}}} Reduce.



So the y-intercept is *[Tex \LARGE \left(0,\frac{5}{6}\right)].



Now let's plot the points *[Tex \LARGE \left(-\frac{10}{3},0\right)] and *[Tex \LARGE \left(0,\frac{5}{6}\right)] which are the x and y intercepts respectively.



{{{drawing(500, 500, -5, 5, -5, 5,
grid(0),
graph(500, 500, -5, 5, -5, 5,0)
circle(-10/3,0,0.03),circle(-10/3,0,0.05),circle(-10/3,0,0.08),circle(-10/3,0,0.10),circle(-10/3,0,0.12),
circle(0,5/6,0.03),circle(0,5/6,0.05),circle(0,5/6,0.08),circle(0,5/6,0.10),circle(0,5/6,0.12)
)}}}



Now draw a straight line through the plotted points to graph {{{3x - 12y = -10}}}.



{{{ drawing(500, 500, -5, 5, -5, 5,
grid(0),
graph(500, 500, -5, 5, -5, 5,(-10-3x)/(-12)),
circle(-10/3,0,0.03),circle(-10/3,0,0.05),circle(-10/3,0,0.08),circle(-10/3,0,0.10),circle(-10/3,0,0.12),
circle(0,5/6,0.03),circle(0,5/6,0.05),circle(0,5/6,0.08),circle(0,5/6,0.10),circle(0,5/6,0.12)
)}}} Graph of {{{3x - 12y = -10}}}