Write an equation of a line that is perpendicular

The distance will be the length of the segment along this line that crosses each of the original lines. However, a vertical line is not a function so the definition is not contradicted.

find the equation of the line that is parallel to this line and passes through the point

So this first piece of information that it's perpendicular to that line right over there. It'll cross where the two lines' equations are equal, so I'll set the non-y sides of the second original line's equaton and the perpendicular line's equation equal to each other, and solve: The above more than finishes the line-equation portion of the exercise.

Find the slope of the function. I'll leave the rest of the exercise for you, if you're interested. Otherwise, they must meet at some point, at which point the distance between the lines would obviously be zero.

what is the equation of the line that passes through (?2, ?3) and is perpendicular to 2x ? 3y = 6?

Then my perpendicular slope will be. Where does this line cross the second of the given lines? We still don't know what the y-intercept of B is, but we can use this information to figure it out.

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Finding Parallel and Perpendicular Lines