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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
- −0.5
Here 'a' represents the slope of the line. Since two parallel lines never intersect each other and they have the same steepness, their slopes are always equal. For example, if the equations of two lines are given as, y = -3x + 6 and y = -3x - 4, we can see that the slope of both the lines is the same (-3). Therefore, they are parallel lines.
Parallel lines are the lines that never intersect each other. Thus, two parallel lines always maintain a constant distance between them. Perpendicular lines are the two lines that intersect each other at a right angle. We come across examples of parallel lines and perpendicular lines in daily life. Observe the white lines or stripes in a marked ...
- Parallel lines are the lines which never intersect each other even if we extend them infinitely whereas intersecting lines meet each other at a point.
- No. Intersecting lines can meet at any angle. But all perpendicular lines are intersecting lines.
- The common characteristic is that both have straight lines.
- Yes. A figure can have both Parallel and Perpendicular Lines. Some examples are: Letter H, Letter E, Square, Rectangle etc.
- A rectangle has 2 pairs of parallel lines and 4 pairs of perpendicular lines.
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 ...
Jan 16, 2024 · Compare the slopes of each line. Remember, when two lines are parallel to each other, they will have the exact same slope. Using the equation y = mx + b where m is the slope of the line, you can identify and compare the slopes of two lines. In our example, the first line has an equation of y = 3x + 5, therefore it’s slope is 3.
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For example, look at these two equations (standard form equations of a line). \begin {align*} 6x + 2y = 10 \\ [1em] 12x + 4y = 20 \end {align*} 6x +2y = 10 12x +4y = 20. They look different and each of them gives the same slope. So you might conclude that they are equations of parallel lines.
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Parallel lines have the same slope. Perpendicular lines have slopes that are opposite reciprocals. In other words, if m = a b, then m ⊥ = − b a. To find an equation of a line, first use the given information to determine the slope. Then use the slope and a point on the line to find the equation using point-slope form.
