Answer
(a) Standard form
$y=1$
(b) Slope-intercept form
$y=1$
Work Step by Step
RECALL:
(1) The standard form of a line's equation is $Ax+By=C$.
(2) 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.
(3) Parallel lines have the same slope.
(4) A line whose equation is of the form $y=k$ is horizontal and parallel to the x-axis. Every point on the line has a y-coordinate $k$.
The line is parallel to the horizontal line $y=-5$. This means the line is also horizontal.
Since the horizontal line contains the point $(4, 1)$, then every point on the line must have a y-coordinate of $1$. Thus, the equation of the line is $y=1$.
(a) Standard form
$y=1$
(b) Slope-intercept form
$y=1$
