Answer
$y=-x+4$
Work Step by Step
RECALL:
(i)
The y-intercept is the y-coordinate of the point where a line passes through the y-axis.
(ii)
The slope-intercept form of the equation of a line is:
$y=mx+b$
where
m=slope
b=y-intercept
The given line passes through the y-axis at $(0, 4)$ therefore its y-intercept is 4.
This means that the tentative equation of the given line is
$y=mx + 4$
The line contains the point $(4, 0)$, to the coordinates of this point satisfy the equation of the line.
Substitute the x and y coordinates of this point into the tentative equation of the line to have:
$y=mx+4
\\0=m(4)+4
\\0=4m+4
\\-4=4m
\\-1 = m$
Therefore, the equation of the line is $y=-x+4$.
