Answer
$y=-\dfrac{1}{2}x+16$
Work Step by Step
We have to determine the equation
$$y=mx+b,$$
where
$y$ represents the flare's length
$x$ represents the burning time.
We are given two points on the graph of the line describing the equation: $(6,13)$ and $(20,6)$.
$\textbf{First method}$
We will write the equation in point-slope form, then rewrite it in slope-intercept form.
We calculate the slope:
$$m=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{6-13}{20-6}=-\dfrac{1}{2}.$$
We determine the point-slope equation using the slope $m$ and one of the points, $(6,13)$:
$$y-y_0=m(x-x_0)$$
$$y-13=-\dfrac{1}{2}(x-6)$$
Rewrite the equation in slope-intercept form:
$$y=-\dfrac{1}{2}x+3+13$$
$$y=-\dfrac{1}{2}x+16$$
$\textbf{Second method}$
We will calculate the slope of the line, then its $y$-intercept and finally write the equation in slope-intercept form.
We calculate the slope:
$$m=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{6-13}{20-6}=-\dfrac{1}{2}.$$
Substitute the slope and the coordinates of one point, for example $(6,13)$, into slope-intercept form and solve for $b$:
$$\begin{align*}
y&=mx+b\\
13&=-\dfrac{1}{2}(6)+b\\
b&=13+3=16.
\end{align*}$$
Substitute $m$ and $b$ into the slope-intercept form:
$$y=-\dfrac{1}{2}x+16.$$
