Answer
(a) slope-intercept form:
$\color{blue}{y=-2x+1}$
(b) standard form:
$\color{red}{2x+y=1}$
Work Step by Step
RECALL:
(1) The slope-intercept form of a line's equation is $y=mx+b$ where $m$=slope and $(0, b)$ is the line's y-intercept.
(2) The standard form of a line's equation is $Ax+By=C$ where $A\ge0$ and A, B, and C are integers.
(3) The point-slope form of a line's equation is $y-y_1=m(x-x_1)$ where $m$=slope and $(x_1, y_1)$ is a point on the line.
The given line has a slope of $-2$ and contains the point $(3, -5)$.
This means the point-slope form of the line's equation is:
$$y-(-5)=-2(x-3)
\\y+5=-2(x-3)$$
(a) slope-intercept form
The slope-intercept form of the line can be derived from the equation above:
$y+5=-2(x-3)
\\y+5=-2(x)-(-2)(3)
\\y+5=-2x+6
\\y+5-5=-2x+6-5
\\\color{blue}{y=-2x+1}$
(b) standard form
The standard form of the line's equation can be derived from the slope-intercept form:
$y=-2x+1
\\y+2x+=-2x+1+2x
\\\color{red}{2x+y=1}$
