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=(3)/(4)`.

`y=m_2x+b\to m_2=(3)/(4)`

`y=(3)/(4)x+b`

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

`-1=(3)/(4)\cdot2+b\\\\-1=(3)/(2)+b\ \ \ \ |-(3)/(2)\\\\b=-(2)/(2)-(3)/(2)\\\\b=-(5)/(2)`

`y=(3)/(4)x-(5)/(2)\ \ \ \ |\cdot4\\\\4y=3x-5\cdot2\ \ \ \ |-3x\\\\-3x+4y=-10\ \ \ \ \ |\cdot(-1)\\\\3x-4y=10`

Answer: 3x - 4y = 10