



 
Hi Karen, In both of your problems you have an equation of the form $ax + by = c$ where $a, b$ and $c$ are constants. The first step is to solve the equation for $y.$ I am going to look at an example $4x + 5y = 6.$ To solve for $y$ I would first add $4x$ to each side and then divide both sides by $5.$ This yields \[y =  \frac{4}{5} x + \frac{6}{5}.\] This is in the form that your textbook probably writes \[y = mx + b.\] In this form $m$ is the slope of the line and hence the line $4x + 5y = 6$ has slope $ \large \frac4{5}.$ If you are looking for a line parallel to this line it must also have a slope of $ \large \frac4{5}$ and hence its equation has the form \[y =  \frac{4}{5} x + b\] for some constant $b.$ Use any other facts you are given to evaluate $b.$ If you are looking for a line perpendicular to $4x + 5y = 6$ this line it must also have a slope which is the negative reciprocal of the slope of $4x + 5y = 6$ and hence its slope is $ \large \frac5{4}$ and hence its equation has the form \[y = \frac{5}{4} x + b\] for some constant $b.$ Use any other facts you are given to evaluate $b.$ Write back if you need more assistance,  


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences. 