Hey there! I'm happy to help!
The slope of a perpendicular line is always the negative reciprocal of the original.
QUESTION 1
For the first one, we have a slope of -2/7. To find the reciprocal you flip the numerator and denominator, giving us -7/2. Then, we want the negative reciprocal, so since two negatives make a positive our perpendicular slope is 7/2.
QUESTION 2
Let's first rearrange our equation to be in slope intercept form.
3x+5y=-15
Subtract 3x from both sides.
5y=-3x-15
Divide both sides by 5.
y=-3/5x-3
First we find the reciprocal of -3/5, which is -5/3. This is the normal reciprocal, but we want the negative one, and since two negatives makes a positive, our slope is 5/3.
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