Answer
$\color{blue}{y=-\dfrac{2}{3}x-\dfrac{1}{3}}$
Work Step by Step
RECALL:
The slope-intercept form of a line's equation is:
$y=mx+b$
where $m$=slope and $b$ = y-intercept.
The line has a slope of $-\dfrac{2}{3}$, so the tentative equation of the line is:
$y=-\dfrac{2}{3}x+b$
To find the value of $b$, substitute the x and y values given in the problem into the tentative equation above to obtain:
$y=-\dfrac{2}{3}x+b
\\-1=-\dfrac{2}{3}(1)+b
\\-1=-\dfrac{2}{3}+b
\\-1+\dfrac{2}{3}=b
\\-\dfrac{3}{3}+\dfrac{2}{3}=b
\\-\dfrac{1}{3}=b$
Therefore, the equation of the line is $\color{blue}{y=-\dfrac{2}{3}x-\dfrac{1}{3}}$.
