Patricia P. answered • 10/12/19

GRE/LSAT/GMAT/SAT/ACT Test prep specialist

Mary,

If two lines are parallel to each other, they both have the same slope. So let us find the slope we are looking for:

5x + 2y = 12

2y = -5x + 12

y = -5/2x + 6

We want a line with slope -5/2, and it has to pass through (-10,3).

We can plug in this given point to solve:

3 = -5/2(-10) + ?

3 = 25 + ?

28 is our answer for that last question and so it is our y-intercept.

So the equation of our first line is y = -5/2x - 22

If two lines are perpendicular, their slopes are negative reciprocals of each other. So first find the slope of the first line:

5x + 3y = 15

3y = -5x + 15

y = -5/3x + 5

Your slope is -5/3 and the negative reciprocal of that is 3/5.

So we are looking for a line with slope 3/5 that goes through point (5,1).

Lets plug this point in, just like last time:

y = mx + b

1 = 3/5(5) + b

1 = 3 + b

b = -2

So the equation of this line is y = 3/5x - 2.

Hope this helps! :)

Patricia P.

10/12/19