Question

Write the equation for the line parallel to the given line 4x-3y=9 and through the point (3, -1). Then Write the answers in slope intercept and standard form

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:

$4x-3y=9\ \ \ \ |-4x\\\\-3y=-4x+9\ \ \ \ |:(-3)\\\\y=\dfrac{4}{3}x-3\to m_1=\dfrac{4}{3}$

$y=m_2x+b\\\\m_2=m_1\to m_2=\dfrac{4}{3}$

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

The line passest through the point (3, -1). Substitute the coordinates of the point to the equation of a line:

$-1=\dfrac{4}{3}\cdot3+b\\\\-1=4+b\ \ \ \ |-4\\\\b=-5$

$y=\dfrac{4}{3}x-5\ \ \ \ |\cdot3\\\\3y=4x-15\ \ \ \ |-4x\\\\-4x+3y=-15\ \ \ \ |\cdot(-1)\\\\4x-3y=15$

Answer: $\boxed{y=\dfrac{4}{3}x-5;\ 4x-3y=15}$