Equation for a linear line: Knowing the coordinates of two points

Question:
A line goes through points (-3, 9) and (2, 4). Find the equation of the linear line.

Answer:
There are two methods. You can use a line equation with two unknowns:
\[
y = ax + b
\]
where $a$ is the slope and $b$ is the intercept. Plug in the coordinates to solve for simultaneous equations.
\begin{eqnarray}
9 &=& -3a + b \\
4 &=& 2a + b
\end{eqnarray}
(1)-(2) gives $5 = -5a$. Thus, $a=-1$. Plug back in either equation and we get $b=6$. The line equation is
\[
y = -x + 6
\]
The other method is to utilize following formula:
\[
(y-y_1)=\frac{y_2-y_1}{x_2-x_1}(x-x_1)
\]
The factor, $\frac{y_2-y_1}{x_2-x_1}$, corresponds to the slope. After plugging in the coordinates, we can obtain the same result.

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