Answer
$a)$ $y=\dfrac{2}{3}x-\dfrac{16}{3}$
$b)$ $2x-3y-16=0$
$c)$
Work Step by Step
The line that passes through the points $(-1,-6)$ and $(2,-4)$
$a)$
The point-slope form of the equation of a line is $y-y_{1}=m(x-x_{1})$, where $(x_{1},y_{1})$ is a point through which the line passes and $m$ is its slope.
Two points through which the line passes are given. Use them to find the slope of the line:
$m=\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}=\dfrac{-4+6}{2+1}=\dfrac{2}{3}$
Substitute the slope found and one of the points given into the point-slope form of the equation of a line formula and simplify:
$y-(-6)=\dfrac{2}{3}[x-(-1)]$
$y+6=\dfrac{2}{3}(x+1)$
$y+6=\dfrac{2}{3}x+\dfrac{2}{3}$
Take $6$ to the right side and simplify to represent the equation in slope-intercept form:
$y=\dfrac{2}{3}x+\dfrac{2}{3}-6$
$y=\dfrac{2}{3}x-\dfrac{16}{3}$
$b)$
To represent the equation in general form, begin by taking $y$ to the right side:
$0=\dfrac{2}{3}x-y-\dfrac{16}{3}$
$\dfrac{2}{3}x-y-\dfrac{16}{3}=0$
Multiply the whole equation by $3$:
$3\Big(\dfrac{2}{3}x-y-\dfrac{16}{3}=0\Big)$
$2x-3y-16=0$
$c)$
