Question 101158


{{{2*x+1*y=4}}} Start with the given equation


Let's find the x-intercept


To find the x-intercept, let y=0 and solve for x:

{{{2*x+1*(0)=4}}} Plug in {{{y=0}}}


{{{2*x=4}}} Simplify


{{{x=4/2}}} Divide both sides by 2



{{{x=2}}} Reduce




So the x-intercept is ({{{2}}},0) (note: the x-intercept will always have a y-coordinate equal to zero)


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{{{2*x+1*y=4}}} Start with the given equation


Now let's find the y-intercept


To find the y-intercept, let x=0 and solve for y:

{{{2*(0)+1*y=4}}} Plug in {{{x=0}}}


{{{1*y=4}}} Simplify


{{{x=4/1}}} Divide both sides by 1




{{{y=4}}} Reduce




So the y-intercept is (0,{{{4}}}) (note: the y-intercept will always have a x-coordinate equal to zero)


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So we have these intercepts:

x-intercept: ({{{2}}},0)


y-intercept: (0,{{{4}}})




Now plot the two points ({{{2}}},0) and (0,{{{4}}}) 


{{{drawing(500, 500, -4, 4, -6, 6,
graph(500, 500, -4, 4, -6, 6,0),
circle(2,0,0.0666666666666667),
circle(2,0,0.0966666666666667),

circle(0,4,0.0666666666666667),
circle(0,4,0.0966666666666667)


)}}}



Now draw a line through the two points to graph {{{2*x+1*y=4}}}

{{{drawing(500, 500, -4, 4, -6, 6,
graph(500, 500, -4, 4, -6, 6,(4-2*x)/1),
circle(2,0,0.0666666666666667),
circle(2,0,0.0966666666666667),

circle(0,4,0.0666666666666667),
circle(0,4,0.0966666666666667)


)}}} graph of {{{2*x+1*y=4}}} through the points ({{{2}}},0) and (0,{{{4}}})