An equation parallel and perpendicular to 4x+5y=19

An equation parallel to 4x + 5y = 19 would be y = - 4/5x + 12.

An equation perpendicular to 4x + 5y = 19 would be y = 5/4x + 10.

Step-by-step explanation:

The equation given represents a linear equation in Standard Form (Ax + By = C). Lines that are parallel to each other go the same direction and don't touch, so their slopes must be the same. However, lines that are perpendicular go in opposite directions and intersect, so their slopes must be the direct opposite of each other. In order to find the slope, you must first convert from the Standard Form given to Slope Intercept Form (y = mx + b). When you solve the given equation for 'y', you get: y = - 4/5x + 19, where the slope = - 4/5. To make a parallel equation, simply keep the same slope and choose a different y-intercept ('b'). To make a perpendicular equation, take the direct opposide of your slope 5/4 (positive) and choose a different y-intercept.