Question

indicate in standard form the equation of the line in standard form. the line through (2,-1) and parallel to a line with slope 3/4

Answer 1

$k:y=m_1x+b_1;\ l:y=m_2x+b_2\\\\k\ \perp\ l\iff m_1\cdot m_2=-1\\\\k\ ||\ l\iff m_1=m_2$

We have $m_1=\dfrac{3}{4}$.

$y=m_2x+b\to m_2=\dfrac{3}{4}$

$y=\dfrac{3}{4}x+b$

The line passes through point (2, -1). Substitute the coordinates of the point to the equation of a line:

$-1=\dfrac{3}{4}\cdot2+b\\\\-1=\dfrac{3}{2}+b\ \ \ \ |-\dfrac{3}{2}\\\\b=-\dfrac{2}{2}-\dfrac{3}{2}\\\\b=-\dfrac{5}{2}$

$y=\dfrac{3}{4}x-\dfrac{5}{2}\ \ \ \ |\cdot4\\\\4y=3x-5\cdot2\ \ \ \ |-3x\\\\-3x+4y=-10\ \ \ \ \ |\cdot(-1)\\\\3x-4y=10$

Answer: 3x - 4y = 10