Question 229567
Determine the x- and y-intercepts (if any) of the given equation. Show your work. Then plot the intercepts, and graph the line;

 
{{{2x + y = 5}}}


Step 1.  Intercepts means that the intersect the x or y axis.  This means that one of the coordinates is zero.  So for x=0, then the point (0,b) has b a the y-intercepts. and for y=0, then the point (a,0) has a as the x-intercept.


Step 2.  Then for x=0 in equation {{{2x + y = 5}}}we have


{{{2*0 + y = 5}}}


{{{y=5}}}


So we have (0,5) as one point with b=5 as the y-intercept.


Step 3.  Then for y=0 in equation {{{2x + y = 5}}} we have


{{{2x + 0 = 5}}}


{{{2x=5}}}


Divide by 2 to both sides of the equation


{{{cross(2)y/cross(2)=5/2}}}


{{{y=5/2}}} or {{{a=5/2}}} 


So we have (5/2, 0) as one point with a=5/2 as the x-intercept.


Step 4.  ANSWER:   So we have (0,5) as one point with b=5 as the y-intercept and we have (5/2,0) as one point with a=5/2 as the x-intercept.


We can use these two points (0,5) and (5/2,0) to plot the graph.


{{{graph(400,400, -10,10, -10, 10, -2x+5)}}}


I hope the above steps were helpful.


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Good luck in your studies!


Respectfully,
Dr J