Answer
$\color{blue}{y=-5x+11}$
Work Step by Step
RECALL:
(1) The slope-intercept form of a line's equation is:
$y=mx+b$
where $m$ = slope and $b$ = y-intercept
(2) The slope of the line that passes through the points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the formula:
$m=\dfrac{y_2-y_1}{x_2-x_1}$
Solve for the slope using the formula in (2) above to obtain:
$m=\dfrac{-4-1}{3-2}=\dfrac{-5}{1}=-5$
Thus, the tentative equation of the line is:
$y=-5x+b$
To find the value of $b$, substitute the values of x and y of the given point $(2, 1)$ to obtain:
$y=-5x+b
\\1=-5(2)+b
\\1=-10+b
\\1+10=b
\\11=b$
Thus, the equation of the line is $\color{blue}{y=-5x+11}$.
