Question 475584


<h4>x-intercept</h4>

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



{{{2x-4y=1}}} Start with the given equation.



{{{2x-4(0)=1}}} Plug in {{{y=0}}}.



{{{2x-0=1}}} Multiply {{{-4}}} and 0 to get 0.



{{{2x=1}}} Simplify.



{{{x=(1)/(2)}}} Divide both sides by {{{2}}} to isolate {{{x}}}.



So the x-intercept is *[Tex \LARGE \left(\frac{1}{2},0\right)].



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



<h4>y-intercept</h4>

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



{{{2x-4y=1}}} Start with the given equation.



{{{2(0)-4y=1}}} Plug in {{{x=0}}}.



{{{0-4y=1}}} Multiply {{{2}}} and 0 to get 0.



{{{-4y=1}}} Simplify.



{{{y=(1)/(-4)}}} Divide both sides by {{{-4}}} to isolate {{{y}}}.



{{{y=-1/4}}} Reduce.



So the y-intercept is *[Tex \LARGE \left(0,-\frac{1}{4}\right)].



Now let's plot the points *[Tex \LARGE \left(\frac{1}{2},0\right)] and *[Tex \LARGE \left(0,-\frac{1}{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(1/2,0,0.03),circle(1/2,0,0.05),circle(1/2,0,0.08),circle(1/2,0,0.10),circle(1/2,0,0.12),
circle(0,-1/4,0.03),circle(0,-1/4,0.05),circle(0,-1/4,0.08),circle(0,-1/4,0.10),circle(0,-1/4,0.12)
)}}}



Now draw a straight line through the plotted points to graph {{{2x-4y=1}}}.



{{{ drawing(500, 500, -10,10,-10,10,
grid(0),
graph(500, 500, -10,10,-10,10,(1-2x)/(-4)),
circle(1/2,0,0.03),circle(1/2,0,0.05),circle(1/2,0,0.08),circle(1/2,0,0.10),circle(1/2,0,0.12),
circle(0,-1/4,0.03),circle(0,-1/4,0.05),circle(0,-1/4,0.08),circle(0,-1/4,0.10),circle(0,-1/4,0.12)
)}}} Graph of {{{2x-4y=1}}}