Answer:
[tex]\large\boxed{y=\dfrac{5}{4}x+7}[/tex]
Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
We have
[tex]y=-\dfrac{4}{5}x+3\to m_1=-\dfrac{4}{5}[/tex]
If [tex]k:y=m_1x+b_1[/tex] and [tex]l:y=m_2x+b_2[/tex], then
[tex]l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}[/tex]
Calculate the slope:
[tex]m_2=-\dfrac{1}{-\frac{4}{5}}=\dfrac{5}{4}[/tex]
Therefore e have the equation of a line:
[tex]y=\dfrac{5}{4}x+b[/tex]
The line passes through the point (4, 12). Put the coordinates of the point to the equation of a line:
[tex]12=\dfrac{5}{4}(4)+b[/tex]
[tex]12=5+b[/tex] subtract 5 from both sides
[tex]7=b\to b=7[/tex]
Finally:
[tex]y=\dfrac{5}{4}x+7[/tex]
