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Graphing Linear Relationships

Graphing Linear Relationships 1.2 - Solution

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Equations written in slope-intercept form follow a specific format. y=mx+b y=mx+b Here, mm represents the slope of the line and bb represents the y-y\text{-}intercept. Let's identify the slope and the y-y\text{-}intercept in our equation. y=mx+by=-12x+5 y={\color{#0000FF}{m}}x+{\color{#009600}{b}} \quad \Leftrightarrow \quad y={\color{#0000FF}{\text{-} \dfrac{1}{2}}}x+{\color{#009600}{5}} The slope is -12{\color{#0000FF}{\text{-} \frac{1}{2}}} and the yy-intercept is 5.{\color{#009600}{5}}.

Graphing the Equation

Since the yy-intercept is 55 we know that the point (0,5)(0,5) is on the graph. We can use that the slope, m,m, is -12\text{-} \frac{1}{2} to find another point on the graph. m=ΔyΔxm=-12=-12 m=\dfrac{{\color{#0000FF}{\Delta y}}}{{\color{#009600}{\Delta x}}} \quad \Rightarrow \quad m=\text{-} \dfrac{1}{2}= \dfrac{{\color{#0000FF}{\text{-} 1}}}{{\color{#009600}{2}}} Thus, we can can find another point by first moving 22 units in the positive horizontal direction and then 11 unit in the negative vertical direction.

To graph the equation we will now connect the two points with a line.

Identify the xx-intercept

Now that we have graphed the given function, we can use our graph to identify the x-x\text{-}intercept. This is the point at which the line intercepts the x-x\text{-}axis.

The line crosses the axis at (10,0),(10,0), so the x-x\text{-}intercept is 10.10.