Answer:
1. y = -(2/5)x - (1/5)
2. y = -(9/5)x - 4
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