Explanation:
the line is perpendicular to
y = 2x.
and it goes through the point (1, 2).
the point-slope form looks like
y - y1 = a(x - x1)
"a"being the slope, and (x1, y1) being a point on the line.
the slope-intercept form is
y = ax + b
"a" is again the slope, "b" is the y-intercept (the y value when x = 0).
as you can see, we need the slope of the new line in both cases.
then we will start with the point-slope form, and transform it into the slope-intercept form.
the slope of a line is generally the ratio (y coordinate change / x coordinate change) when going from one point on the line to another.
it is always the factor of x.
we can see it is 2 for the original line. that means 2/1.
a perpendicular slope is turning the x and y values upside down, and is flipping the sign.
so, in our case it is
-1/2
so, starting with the new slope and the point to create the point-slope form :
y - 2 = -1/2 × (x - 1)
and from there we transform into the slope-intercept form :
2y - 4 = -x + 1
2y = -x + 5
y = (-x + 5)/2 = -1/2 x + 5/2 = -1/2 × (x - 5)
all of the expressions in the last line are valid forms to write it.