Question

Question #84641

Answer 1

6 hours

Explanation:

`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`