Question 229568
Determine the x- and y-intercepts (if any) of the given equation. Show your work. Then plot the intercepts, and graph the line; 


{{{-x + 2y = 4}}}


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 {{{-x + 2y = 4}}} we have


{{{-0 + 2y = 4}}}


{{{2y=4}}}


Divide by 2 to both sides of the equation


{{{cross(2)y/cross(2)=4/2}}}


{{{y=2}}}


So we have (0,2) as one point with b=-7 as the y-intercept.


Step 3.  Then for y=0 in equation {{{-x + 2y = 4}}} we have


{{{x + 2*0 = 4}}}


{{{x=4}}} or {{{a=4}}} 


So we have (4, 0) as one point with a=4 as the x-intercept.


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


We can use these two points (0,2) and (4,0) to plot the graph.


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


I hope the above steps were helpful.


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Good luck in your studies!


Respectfully,
Dr J