1.12.6 Choosing a Method to Write an Equation

Compare your answer:

Your answer may vary, but here is a sample. You will use the point-slope form to find the line $y-y_1=m(x-x_1)$ given the two points on your slip.

Points $(3,4)$ and $(6,2)$

$\begin{array}{ccc}\hfill y-y_1& \hfill =\hfill & m(x-x_1)\hfill \\ \hfill y-(4)& \hfill =\hfill & m(x-(3))\hfill \\ \hfill (6)-4& \hfill =\hfill & m((2)-3)\hfill \\ \hfill 2& \hfill =\hfill & m(-1)\hfill \\ \hfill 2& \hfill =\hfill & -m\hfill \\ \hfill m& \hfill =\hfill & -2\hfill \end{array}$

Points $(-3,-4)$ and $(6,2)$

$\begin{array}{ccc}\hfill y-y_1& \hfill =\hfill & m(x-x_1)\hfill \\ \hfill y-(-4)& \hfill =\hfill & m(x-(-3))\hfill \\ \hfill (6)+4& \hfill =\hfill & m((2)+3)\hfill \\ \hfill 10& \hfill =\hfill & m(5)\hfill \\ \hfill 10& \hfill =\hfill & 5m\hfill \\ \hfill m& \hfill =\hfill & 2\hfill \end{array}$

Compare your answers: Your answers may vary, but here are some samples.

Points: $(3,4)$ and $(6,2)$ $y-2=-\frac{2}{3}(x-6)$ $y-4=-\frac{2}{3}(x-3)$

Points: $(‒3,‒4)$ and $(6,2)$ $y-2=-\frac{2}{3}(x-6)$ $y+4=-\frac{2}{3}(x+3)$

Equations with no match: $y+4=-\frac{2}{3}(x+3)$ $y-4=-\frac{2}{3}(x-3)$

Compare your answer:

Your answer may vary, but here is a sample. No, the slope is not enough to identify the equation, because lines with the same slope can go through different points.