What is the equation of the line, in slope-intercept form, that passes through the point (0,7) and is perpendicular to the line y=3x−5?
y=−13x−5
y=−5x−5
y=−3x+7
y=−13x+7
y=3x+7
y=−5x+7

A line perpendicular to another occurs at the negative reciprocal of the slope of the original line. Why this is, I can further explain in the comments if you're interested. What is a reciprocal though? a reciprocal, if you're unfamiliar, is just the flipped form of it.

As an example, the negative reciprocal of 1/4 is -4/1. I multiplied 1/4 by a negative, and flipped the fraction.

So, what would the negative reciprocal of 3 be? well, you can imagine 3 to be 3/1 to help. so we multiply it by a negative, which gives us -3/1, and then we flip it, giving us -1/3. This is the slope of our unknown line. Because of this, we can mark out...well all of them haha. You need to double check your question and answers provided. With the info you've given me, none of your answers are correct. Let me know what happened if you can! if not, I would question your teacher, cause they messed up somewhere haha.