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This line has some slope value (though not a value of "2", of course, because this line equation isn't solved for " y="). Parallel and perpendicular lines 4-4. The lines have the same slope, so they are indeed parallel. I'll solve for " y=": Then the reference slope is m = 9. It was left up to the student to figure out which tools might be handy. The distance will be the length of the segment along this line that crosses each of the original lines.
In other words, to answer this sort of exercise, always find the numerical slopes; don't try to get away with just drawing some pretty pictures. Now I need to find two new slopes, and use them with the point they've given me; namely, with the point (4, −1). Perpendicular lines and parallel lines. Hey, now I have a point and a slope! The other "opposite" thing with perpendicular slopes is that their values are reciprocals; that is, you take the one slope value, and flip it upside down. Then the full solution to this exercise is: parallel: perpendicular: Warning: If a question asks you whether two given lines are "parallel, perpendicular, or neither", you must answer that question by finding their slopes, not by drawing a picture!
Share lesson: Share this lesson: Copy link. Therefore, there is indeed some distance between these two lines. 7442, if you plow through the computations. I'll find the values of the slopes. The distance turns out to be, or about 3. For the perpendicular line, I have to find the perpendicular slope. To answer the question, you'll have to calculate the slopes and compare them. Remember that any integer can be turned into a fraction by putting it over 1. The result is: The only way these two lines could have a distance between them is if they're parallel. In other words, these slopes are negative reciprocals, so: the lines are perpendicular. Or continue to the two complex examples which follow.
Are these lines parallel? 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. For the perpendicular slope, I'll flip the reference slope and change the sign. 99, the lines can not possibly be parallel.
Or, if the one line's slope is m = −2, then the perpendicular line's slope will be. I know I can find the distance between two points; I plug the two points into the Distance Formula. It's up to me to notice the connection. Then the answer is: these lines are neither.