Question

Looking for help on how to find the slope-intercept form that is perpendicular to the given line.

4x-2y=3
(2,1)

Answer 1

u have
\[\large 4x-2y=3 \]
which can be rewritten as
\[\large 2y=4x-3\qquad\text{or}\qquad y=2x-\frac{3}{2} \]
this is the slope-intercept form. this line has slope m=2

Answer 2

now, a line perpendicular to the given one has slope m1 that satisfies:
\[\large -1=m\cdot m_1=2m_1\qquad\text{so}\qquad m_1=-\frac{1}{2} \]
so it slope-intercept equation would be:
\[\large y=-\frac{1}{2}x+b\tag{*}\]

Answer 3

finaly, since this line has to pass through (2,1) replace x=2 and y=1 in (*) to get the value of b:
\[\large 1=-\frac{1}{2}\cdot2+b\qquad\Rightarrow\qquad b=2 \]
So the equation u r looking for is
\[ \large y=-\frac{1}{2}x+2 \]