# Question #84641

Apr 2, 2017

6 hours

#### Explanation:

$\textcolor{b l u e}{\text{Using visual assessment}}$

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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$\textcolor{b l u e}{\text{Using mathematical assessment}}$

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

$y = m x + c$

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

By observation the y-intercept is 9 $\to y = m x + 9$

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

$m \to \left(\text{change in sleeping")/("change in TV}\right) \to \frac{0 - 9}{9 - 0} = - 1$

So we now have: $y = \left(- 1\right) x + 9 \text{ "->" } y = - x + 9$

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

$y = - x + 9 \text{ "->" } y = - 3 + 9 = 6$