Section 1 - Topic 9 Parallel and Perpendicular Lines - Part 2 (please help) 1. Write the equation of the line that it is perpendicular to y = 7x - 3 and passes through the origin.

2. Write the equation of the line that it is parallel to y = 2x + 1 and passes through the solution of the following system of equations. (3x - 2y = 10 x + y = 5

9514 1404 393

Step-by-step explanation:

1. The slope of the given line is the x-coefficient, 7. The slope of the perpendicular line is the negative reciprocal of this: -1/7. Since the line goes through the origin, the y-intercept is zero.

  y = -1/7x

__

2. The first part of this problem is to find the solution to the given system of equations. We can substitute for x to do that:

  3(5 -y)-2y = 10

  15 -5y = 10 . . . simplify

  -3 +y = -2 . . . . divide by -2

  y = 1, x = 4 . . . add 3 to find y; subtract y from 5 to find x

__

The second part of this problem requires we note the slope of the parallel line. It is the x-coefficient, 2. The y-intercept can be found from ...

  b = y -mx = 1 -2(4) = -7

So, the desired line in y=mx+b form is ...

  y = 2x -7

_____

The first attachment shows the perpendicular lines of problem 1.

The second attachment shows the parallel lines of problem 2.

step-by-step explanation:

to find if any function is an inverse of the other, put the first equation in as x in the next one. then simplify and solve. if at the end you get the statement y = x, then it is an inverse. if you get anything else, it is not.