The figures given tell us the values when x is 0 and lowest value of y, so let us check these solutions..

\(\frac{1}{2}(y-1)=|x-4|\)

(1) when x is 0
\(\frac{1}{2}(y-1)=|0-4|=|-4|=4........(y-1)=2*4=8....y=8+1=9\)
Look at the choices where the line cuts y-axis at 9
Only C and D are left..
(2) lowest value of y..
As |x-4| is atleast 0 and that is at X=4..
C is out as it gives the lowest value at -4

Hence D

Thanks, could you please explain why we are going to look for lowest value of y?

Hi

If we put Y=0 then we get X = 3.5 and 4.5 . This implies that the graph must intersect the X axes at these 2 points.
Therefore I got confused b/w answer choices.

Am I missing something. Kindly help.

Regards

The equation is: (1/2)(y - 1) = |x - 4|
If y = 0, we get: (1/2)(0 - 1) = |x - 4|
Simplify to get: -0.5 = |x - 4|
Since the absolute value of x-4 can never be negative, there are no solutions to the equation -0.5 = |x - 4|
This tells us that The graph of the equation does NOT intersect the x-axis

This means we can eliminate answer choices A and E, since those graphs cross the x axis

An easy approach for me whenever I'm dealing with graph equations is to always make it as y = ax + b

So simplify it and make it look like y = 2|x-4| + 1

Now take values of x and find it's corresponding y

if x=o => y = 2| - 4| + 1 => y = 2(4) + 1 = 9

if x=+4 => y = 2|0| + 1 => y = + 1

and if you check the graphs for these points you find that only D satisfy this immutable relation.

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