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

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

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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

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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

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The first attachment shows the perpendicular lines of problem 1.

The second attachment shows the parallel lines of problem 2.