Question #84641

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Answer 1 · 2017-04-02T09:19:06

6 hours

#color(blue)("Using visual assessment")#

Notice that the line intercepts the bottom axis at 9 and also the side axis at 9.

This condition is means that the value you select for one axis relates to the same value on the other axis.

Thus 3 hours watching TV relates to 6 hours sleeping.

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#color(blue)("Using mathematical assessment")#

One of the standardised forms for the equation of a strait line is:

#y=mx+c#

where #m# is the slope (gradient) and #c# is the y-intercept.

By observation the y-intercept is 9 #->y=mx+9#

#m# is the slope (gradient) reading left to right on the bottom axis

#m->("change in sleeping")/("change in TV") -> (0-9)/(9-0) =-1#

So we now have: #y=(-1)x+9" "->" "y=-x+9#

We need the value of #y# when sleep is 3 hours

#y=-x+9" "->" "y=-3+9=6#

Tony B