Question

POS What is the equation of the line that is parallel to the line 12x + 15y = 10 and passes through the point (5,-2)?

Answer 1

To find the equation we need the slope and one point. The point is (5,-2) and the slope is the same as the slope of 12x+15y=10. To do this, we solve for x

$\begin{gathered} 12x+15y=10 \\ 15y=-12x+10 \\ y=-\frac{12}{15}x+\frac{10}{15} \\ y=-\frac{4}{5}x+\frac{2}{3} \end{gathered}$

then, the slope is -4/5. So, the equation is

$\begin{gathered} y-(-2)=-\frac{4}{5}(x-5) \\ y+2=-\frac{4}{5}x+4 \\ 5y+10=-4x+20 \\ 4x+5y=10 \end{gathered}$

then, the equation is 4x+5y=10