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Gelneren [198K]
3 years ago
6

The graph of y= - 1/2x+2 is positive over the interval (4, infinity) and negative over the interval (-infinity, 4) .What happens

on the graph when x=4? explain

Mathematics
1 answer:
vichka [17]3 years ago
3 0

The graph of y=ax+b, where a≠0, is always a line:

i) increasing if a>0
ii) decreasing if a<0

Consider the decreasing case.

The line is above the x-axis, that is positive but decreasing. At 1 single point it cuts the x-axis, so x=0, and then it continues decreasing below the x-axis.


Back to our problem:

The graph of y=-1/2 x +2 is a decreasing line.,

so it CANNOT be
"positive over the interval (4, infinity) and negative over the interval (-infinity, 4)"

it is 

"<span>negative over the interval (4, infinity) and  positive over the interval (-infinity, 4)</span>"



the graph is "<span>positive over the interval (-infinity, 4)</span>", it means that the line is decreasing but above the x-axis until 4, (4 not included).

then, "negative over the interval (4, infinity)", which means that the line is now decreasing below the x-axis.

when x=4, the line cuts the x-axis.


check the graph of the line generated using desmos.com

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