Answer: y=1/2(x)-6=0.5x-6
Step-by-step explanation: y=mx+c is the general equation of a straight line.
We are told that the line passes through the point (2, -5) this means at x=2 and y=-5
We need to substitute these into the general equation. This gives us the following:
y=mx+c
-5=m*2+c
To solve for c where the graph cuts the y -axis we need to -2m from both sides
-5-2m=2m-2m+c
-5-2m=c
Places this back into the general equation of a straight line gives us the following
y=mx-5-2m
this is the same as
y=m(x-2)-5........we take out a common factor of m
Now we want the above line to be parallel to x-2y=16
To see this we must put the above equation into the form y=mx+c
x-2y=16
We need to make y the subject that is solve for y or have y on its own
To get y term on its own we need to subtract x from both sides
x-x-2y=16-x
-2y=16-x
To finally get y on its own we need to divide both sides by -2
-2y/-2=16/-2 -x/-2
y=-8+x/2
y=x/2-8
this is the same as
y=1/2(x)-8
Therefore m=1/2
we now substitute this back into the previous original equation to get the following
y=1/2(x-2)-5
y=1/2(x)-1-5
y=1/2(x)-6