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Writing Linear Equations in Point-Slope Form

Writing Linear Equations in Point-Slope Form 1.1 - Solution

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a

Our equation is written in point-slope form. yy1=m(xx1)\begin{gathered} y-y_1=m(x-x_1) \end{gathered} Here, mm is the slope and (x1,y1)(x_1,y_1) is a point on the line. Let's rewrite the given equation to match the above format. y+10=56(x2)y(-10)=56(x2)\begin{aligned} y+10= \dfrac{5}{6}(x-2)\quad\Leftrightarrow\quad y-(\text{-}10)= \dfrac{5}{6}(x-2) \end{aligned} Now, we can identify the slope, m,m, and one of the points. Slope:   m=56Point:   (2,-10)\begin{aligned} \textbf{Slope: }& \ \ m=\dfrac{5}{6}\\ \textbf{Point: }& \ \ (2,\text{-}10) \end{aligned}

b
In point-slope form, mm is the slope and the point (x1,y1)(x_1,y_1) lies on the line. Thus, to find the slope and one point, let's rewrite our equation in this form.

y34=-2(x+1)y34=-2(x(-1))\begin{aligned} y-\dfrac{3}{4}= \text{-}2(x+1)\quad\Leftrightarrow\quad y-\dfrac{3}{4}= \text{-}2(x-(\text{-}1)) \end{aligned} We can now identify the slope as m=-2m=\text{-}2 and one point as (-1,34).\left(\text{-}1,\frac{3}{4}\right).