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Question

# In three hours, James read 18 pages of his history book. In four hours, he read 21 pages. Write the equation of the line that passes through the two points that represent the data in the problem. Use the equation to predict how many pages James will read in six hours.

Solution

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Since the line passes through the two points (3, 18) , (4, 21)

And the line equation is given in the form:

$\color{#4257b2}\dfrac{y-y_{1}}{x-x_{1}} = \dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}$

So, at (3, 18), (4, 21) the line equation will be:

$\dfrac{y-18}{x-3} = \dfrac{21-18}{4-3}$

$\dfrac{y-18}{x-3} = \dfrac{3}{1}$

By using cross multiplication property, then:

$(y-18) =3( x-3)$

$y-18 =3x-9$

Add 18 to both sides, then the line equation will be:

$y =3x+9$

At $x = 6$ hours, then:

$y = (3 \cdot 6) + 9 =18 + 9$

$\therefore\ y= 27\ \text{pages}$

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