Precalculus, Chapter 1, 1.3, Section 1.3, Problem 40

Determine an equation of the line $L$.







Using the formula for slope, $\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1}$, where $(x_1, y_1) = (-1,1)$ and $(x_2, y_2) = (2,2)$. So we have

$\displaystyle m = \frac{2-1}{2-(-1)} = \frac{1}{3}$

The slope is $\displaystyle \frac{1}{3}$.

Using Point Slope Form, $y - y_1 = m(x - x_1)$, where $m$ is the slope and $(x_1, y_1)$ is a point in the line. So we have


$
\begin{equation}
\begin{aligned}

y - 1 =& \frac{1}{3} [x - (-1)]
\\
\\
y - 1 =& \frac{1}{3} (x+1)
\\
\\
y =& \frac{1}{3} x + \frac{1}{3} + 1
\\
\\
y =& \frac{1}{3}x + \frac{4}{3}

\end{aligned}
\end{equation}
$