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Find the equation of the line that is: parallel to y = 2x + 1. and passes though the point (5,4) The slope of y = 2x + 1 is 2. The parallel line needs to have the same slope of 2. We can solve it by using the "point-slope" equation of a line: y − y1 = 2 (x − x1) And then put in the point (5,4): y − 4 = 2 (x − 5)
- Slope
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Jan 16, 2024 · 3. Plug the points for each line into the slope formula. To actually calculate the slope, simply plug in the numbers, subtract, and then divide. Take care to plug in the coordinates to the proper X and Y value in the formula. [6] To calculate the slope of line l: slope = (5 – 4)/ (1 – (-2)) Subtract: slope = 1/3.
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Lines with the same slope are parallel. Hence, the given lines are parallel. Perpendicular lines: Let's consider another set of equations. y = 2x +3 and 4y = –2x+10. On comparing y = 2x +3 and 4y = –2x+10 with y = mx + c . The slopes are m = 2 and m = –1/2. If the slope of one line is the negative reciprocal of the second line, then lines ...
As with parallel lines, we can determine whether two lines are perpendicular by comparing their slopes. The slope of each line below is the negative reciprocal of the other so the lines are perpendicular. f (x) = 1 4x+2 negative reciprocal of 1 4 is −4 f (x) = −4x+3 negative reciprocal of −4 is 1 4 f (x) = 1 4 x + 2 negative reciprocal of ...
Mar 31, 2018 · Telling the Difference Between Parallel and Perpendicular. When two lines (or two sides of a polygon) are parallel, their slopes will be equal. When two lines (or two diagonals of a polygon) are perpendicular, their slopes will be opposite reciprocals of each other. The table below encapsulates this information. Examples.
Parallel Lines: The lines are parallel if their slopes are equal or the same. That means. Perpendicular Lines: The lines are perpendicular if their slopes are opposite reciprocals of each other. Or, if we multiply their slopes together, we get a product of – \,1. These lines intersect at a ninety-degree angle, 90°.
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Parallel lines and their slopes are easy. Since slope is a measure of the angle of a line from the horizontal, and since parallel lines must have the same angle, then parallel lines have the same slope — and lines with the same slope are parallel. Perpendicular lines are a bit more complicated. If you visualize a line with positive slope (so ...
