Exercise 43 Page 79

Equations written in slope-intercept form follow a specific format. y=mx+ b In this form, m represents the slope of the line and b represents the $y\text{-}$intercept.

Identifying Slope and Intercept

Since the given equation is not in slope-intercept form, let's rewrite it so that it will be easier to identify the slope and $y\text{-}$intercept.

Below we highlight the slope $\textcolor{darkorange}{m}$ and $y\text{-}$intercept $\colIII{b}.$ \begin{gathered} y=\textcolor{darkorange}{\N2}x\ \colIII{-}\ \colIII{1}\quad\Leftrightarrow\quad y=\textcolor{darkorange}{\N2}x+(\colIII{\N1}) \end{gathered} The slope is $\textcolor{darkorange}{\N2}.$ The $y\text{-}$intercept is $\colIII{\N 1},$ so the graph crosses the $y\text{-}$axis at the point $(0,\colIII{\N 1}).$

Graphing the Equation

A slope of $\textcolor{darkorange}{\N2}$ means that for every $1$ unit we move in the positive horizontal direction, we move $2$ units in the negative vertical direction. \begin{gathered} \textcolor{darkorange}{m}=\textcolor{darkorange}{\dfrac{\N2}{1}}\quad\Leftrightarrow\quad\dfrac{\textcolor{teal}{\text{rise}}}{\textcolor{magenta}{\text{run}}}=\dfrac{\textcolor{teal}{\N2}}{\textcolor{magenta}{1}} \end{gathered} To graph the equation, plot the $y\text{-}$intercept and then use the slope to find another point on the line.