Question 202174

<h4>x-intercept</h4>

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



{{{-x + 3y = -9}}} Start with the given equation.



{{{-x + 3(0) = -9}}} Plug in {{{y=0}}}.



{{{-x + 0 = -9}}} Multiply {{{3}}} and 0 to get 0.



{{{-x = -9}}} Simplify.



{{{x=(-9)/(-1)}}} Divide both sides by {{{-1}}} to isolate {{{x}}}.



{{{x=9}}} Reduce.



So the x-intercept is *[Tex \LARGE \left(9,0\right)].



------------------------------------------



<h4>y-intercept</h4>

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



{{{-x + 3y = -9}}} Start with the given equation.



{{{-0 + 3y = -9}}} Plug in {{{x=0}}}.



{{{ 3y = -9}}} Simplify.



{{{y=(-9)/(3)}}} Divide both sides by {{{3}}} to isolate {{{y}}}.



{{{y=-3}}} Reduce.



So the y-intercept is *[Tex \LARGE \left(0,-3\right)].



Now plot the points we just found



{{{ drawing(500, 500, -10, 10, -10, 10,
 grid(1),
 graph( 500, 500, -10, 10, -10, 10,0)
 circle(9,0,0.05),   circle(9,0,0.08),circle(9,0,0.12),circle(9,0,0.15),circle(9,0,0.18),

circle(0,-3,0.05), circle(0,-3,0.08),circle(0,-3,0.12),circle(0,-3,0.15),circle(0,-3,0.18)

)}}}



Now draw a line through those two points to graph the equation {{{-x + 3y = -9}}}


{{{ drawing(500, 500, -10, 10, -10, 10,
 grid(1),
 graph( 500, 500, -10, 10, -10, 10,(-9+x)/(3))
 circle(9,0,0.05),   circle(9,0,0.08),circle(9,0,0.12),circle(9,0,0.15),circle(9,0,0.18),

circle(0,-3,0.05), circle(0,-3,0.08),circle(0,-3,0.12),circle(0,-3,0.15),circle(0,-3,0.18)
)}}} 


Graph of {{{-x + 3y = -9}}} with the x-intercept of (9,0) and the y-intercept of (0, -3)