Question

Input the equation of the given line in standard form. The line through (1, -4) and parallel to 2x +3y = 4.

Answer 1

Parallel lines have same slope, use differentiation to find the slope of the equation and then create an equation for line using the point (1,-4)

\[y=\frac{ (4-2x) }{ 3 } \rightarrow y=\frac{ 4 }{ 3 }-\frac{ 2x }{ 3 }\]
\[y'=-\frac{ 2 }{ 3 }\] is the slope of the parallel line.
\[y-y0=m(x-x0) \rightarrow y-1=-\frac{ 2 }{ 3 }[x-(-4)] \rightarrow y=-\frac{ 2 }{ 3 }x-\frac{ 8 }{ 3 }+1\rightarrow\]
\[y=\frac{ -2x-8 }{ 3 }+1 \rightarrow y=\frac{-2x-8+3 }{ 3 } \rightarrow 3y+2x=-5 \]

Answer 2

If you have not covered differentiation, you don't need to worry, just look for slope in the equation \[y=\frac{ -2x }{ 3 }+\frac{ 4 }{ 3 }\] which is in form of \[y=mx+c\] where "m" is the slope, and for sure the slope is "-2/3"