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# Writing Linear Functions

## Writing Linear Functions 1.4 - Solution

a
We can calculate the slope by substituting the given points into the slope formula. $m = \dfrac{y_2-y_1}{x_2-x_1}$ In the above equation, $(x_1,y_1)$ and $(x_2,y_2)$ represent two points on the line. For the line we want to study the points $(9,11)$ and $(\text{-} 3,\text{-} 5)$ are known. Let's find the slope of the line.
$m=\dfrac{y_2-y_1}{x_2-x_1}$
$m=\dfrac{{\color{#009600}{\text{-}5}}-{\color{#0000FF}{11}}}{{\color{#009600}{\text{-}3}}-{\color{#0000FF}{9}}}$
$m=\dfrac{\text{-}16}{\text{-}12}$
$m=\dfrac{16}{12}$
$m=\dfrac{4}{3}$
The slope of the line that passes through the given points is $\frac{4}{3}.$
b
In order to determine the slope of the line that passes through the given points, we will use the slope formula. $m = \dfrac{y_2-y_1}{x_2-x_1}$ In the formula, $m$ represents the slope, and $(x_1,y_1)$ and $(x_2,y_2)$ represent points that lie on the line. The points we will use here are $(\text{-} 13,14)$ and $(17,\text{-} 14).$
$m=\dfrac{y_2-y_1}{x_2-x_1}$
$m=\dfrac{{\color{#009600}{\text{-}14}}-{\color{#0000FF}{14}}}{{\color{#009600}{17}}-({\color{#0000FF}{\text{-} 13}})}$
$m=\dfrac{\text{-}14-14}{17+13}$
$m=\dfrac{\text{-}28}{30}$
$m=\dfrac{\text{-}14}{15}$
$m=\text{-}\dfrac{14}{15}$
The slope of the line that passes through the given points is $\text{-}\frac{14}{15}.$
c
Next, we will find the slope of the line passing through the points $(8,\text{-} 6)$ and $(11,\text{-} 6).$ We will do that using the slope formula. $m = \dfrac{y_2-y_1}{x_2-x_1}$ Let's substitute the values into the formula and calculate the slope.
$m=\dfrac{y_2-y_1}{x_2-x_1}$
$m=\dfrac{{\color{#009600}{\text{-}6}}-({\color{#0000FF}{\text{-}6}})}{{\color{#009600}{11}}-{\color{#0000FF}{8}}}$
$m=\dfrac{\text{-}6+6}{11-8}$
$m=\dfrac{0}{3}$
$m=0$
The slope of the line that passes through the given points is $0.$ It means that the line is horizontal.