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Writing Linear Functions

Writing Linear Functions 1.4 - Solution

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a
We can calculate the slope by substituting the given points into the slope formula. m=y2y1x2x1 m = \dfrac{y_2-y_1}{x_2-x_1} In the above equation, (x1,y1)(x_1,y_1) and (x2,y2)(x_2,y_2) represent two points on the line. For the line we want to study the points (9,11)(9,11) and (-3,-5)(\text{-} 3,\text{-} 5) are known. Let's find the slope of the line.
m=y2y1x2x1m=\dfrac{y_2-y_1}{x_2-x_1}
m=-511-39m=\dfrac{{\color{#009600}{\text{-}5}}-{\color{#0000FF}{11}}}{{\color{#009600}{\text{-}3}}-{\color{#0000FF}{9}}}
m=-16-12m=\dfrac{\text{-}16}{\text{-}12}
m=1612m=\dfrac{16}{12}
m=43m=\dfrac{4}{3}
The slope of the line that passes through the given points is 43.\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=y2y1x2x1 m = \dfrac{y_2-y_1}{x_2-x_1} In the formula, mm represents the slope, and (x1,y1)(x_1,y_1) and (x2,y2)(x_2,y_2) represent points that lie on the line. The points we will use here are (-13,14)(\text{-} 13,14) and (17,-14).(17,\text{-} 14).
m=y2y1x2x1m=\dfrac{y_2-y_1}{x_2-x_1}
m=-141417(-13)m=\dfrac{{\color{#009600}{\text{-}14}}-{\color{#0000FF}{14}}}{{\color{#009600}{17}}-({\color{#0000FF}{\text{-} 13}})}
m=-141417+13m=\dfrac{\text{-}14-14}{17+13}
m=-2830m=\dfrac{\text{-}28}{30}
m=-1415m=\dfrac{\text{-}14}{15}
m=-1415m=\text{-}\dfrac{14}{15}
The slope of the line that passes through the given points is -1415.\text{-}\frac{14}{15}.
c
Next, we will find the slope of the line passing through the points (8,-6)(8,\text{-} 6) and (11,-6).(11,\text{-} 6). We will do that using the slope formula. m=y2y1x2x1 m = \dfrac{y_2-y_1}{x_2-x_1} Let's substitute the values into the formula and calculate the slope.
m=y2y1x2x1m=\dfrac{y_2-y_1}{x_2-x_1}
m=-6(-6)118m=\dfrac{{\color{#009600}{\text{-}6}}-({\color{#0000FF}{\text{-}6}})}{{\color{#009600}{11}}-{\color{#0000FF}{8}}}
m=-6+6118m=\dfrac{\text{-}6+6}{11-8}
m=03m=\dfrac{0}{3}
m=0m=0
The slope of the line that passes through the given points is 0.0. It means that the line is horizontal.