Question

HELP ASAP GEOMETRY . . . . . .

Answer 1

Answer:

1.  y = -(2/5)x - (1/5)

2. y = -(9/5)x - 4

Step-by-step explanation:

For 1:

Step 1:  rewrite the equation of the given line in to slop-intercept form by solving for y

 2x + 5y = 15    

     5y = -2x + 15               (subtract 2x from both sides)

        y = -(2/5)x + 3           (divide both side by 5)

Step 2:  Our line is parallel to this line, so it has the same slope, but a different  y-intercept, so set up the equation...

  y = -(2/5)x + b      

We are given a  point (x, y) of (2, -1), so plug that in and solve for b.

 -1 = -(2/5)(2) + b

    -1 = -4/5 + b      (simplify)

        4/5 -1 = b      (add 4/5 to both sides to isolate b)

        4/5 - 5/5 = b

             -1/5 = b            

So the equation of our line is  y = -(2/5)x - (1/5)

For 2:  

Step 1:  Perpendicular lines have slopes that are opposite reciprocals of each other.  That means you take the slope, flip the fraction, and change the sign.

Here our given line is y = (5/9)x - 4 so the slope 5/9

The opposite reciprocal of 5/9 is -9/5

We set up the equation

y = -(9/5)x + b      

  we are given a point (x, y) of (-5, 5), so plug that in and solve for b

5 = -(9/5)(-5) + b

    5 = 9 + b

     -4 = b  

So our equations is  y = -(9/5)x - 4