how to find the equations of perpendicular lines?
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Perpendicular lines have opposite-reciprocal slopes, so the slope of the line we want to find is 1/2. Plugging in the point given into the equation y = 1/2x + b and solving for b, we get b = 6. Thus, the equation of the line is y = ½x + 6. Rearranged, it is –x/2 + y = 6.
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The slope of the perpendicular line is the negative reciprocal. This means you change the sign of the slope to its opposite: in this case to 3. Then find the reciprocal by switching the denominator and numerator to get 1/3; therefore the slope of the perpendicular line is 1/3.
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Correct answer: Two lines are perpendicular if and only if their slopes are negative reciprocals. To find the slope, we must put the equation into slope-intercept form, , where equals the slope of the line.
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Yes, for two lines to be perpendicular to each other, they must always intersect each other at 90 degrees. If they intersect each other at greater than or less than 90 degrees the lines aren't termed perpendicular.
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['Choose an X coordinate.', 'Use the value from (1) to find the Y coordinate for equations 1 and 2.', 'The distance between the two lines at this point is the absolute value of y1 - y2.']
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['Since the value of m is unknown, the first step is to calculate the slope of the line. ... ', 'Choose (x1, y1) = (–2, –5) and (x2, y2) = (6, 1).', 'By substituting the value obtained in the slope-intercept form, you get the equation:', 'STEP 4: The value of b is still unknown. ... ', 'STEP 5: Now, solve the equation for b.']
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['Find the slope using the given points.', 'Put the value of the slope in the expression of the line i.e. y = mx + c.', 'Now find the value of c using the values of any of the given points in the equation y = mx + c.', 'To find the x-intercept, put y = 0 in y = mx + c.', 'To find the y-intercept, put x = 0 in y = mx + c.']
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If a line is parallel to a plane, it will be perpendicular to the plane's normal vector (just like any other line contained within the plane, or parallel to the plane). To find if two vectors are perpendicular, just take their dot product. If it equals 0, then they are perpendicular.
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Perpendicular lines have slopes that are opposite reciprocals of each other. Therefore, the slope of the line is -2.
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Hence, the equation of a line perpendicular to x axis is x = c. Note : If the line is passing through some other value on x axis, we have to replace "c" by that value.
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The slope-intercept form is y=mx+b y = m x + b , where m m is the slope and b b is the y-intercept. Using the slope-intercept form, the slope is 4 4 . The equation of a perpendicular line to y=4x−5 y = 4 x - 5 must have a slope that is the negative reciprocal of the original slope.
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Find the Equation of a Line Given That You Know Two Points it Passes Through. The equation of a line is typically written as y=mx+b where m is the slope and b is the y-intercept. If you know two points that a line passes through, this page will show you how to find the equation of the line.
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We can determine from their equations whether two lines are parallel by comparing their slopes. If the slopes are the same and the y-intercepts are different, the lines are parallel. If the slopes are different, the lines are not parallel. Unlike parallel lines, perpendicular lines do intersect.
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['A standard form equation is when it is set up.', 'Ax + By = C.', '6x + 2y = 4.', 'A slope-intercept form equation is when it is set up y=mx+b.', 'Y = - 3x + 2.', '4y = -8x + 16 then divide all by 4.', 'y = -2x + 4 slope form.', 'Example 2:']
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Correct answer: Explanation: The question puts the line in point-slope form y – y1 = m(x – x1), where m is the slope. Therefore, the slope of the original line is 1/2. A line perpendicular to another has a slope that is the negative reciprocal of the slope of the other line.
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Two non-vertical lines are perpendicular if the slope of one is the negative reciprocal of the slope of the other. If the slope of the first equation is 4, then the slope of the second equation will need to be for the lines to be perpendicular.
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To find the slope of the given line we need to get the line into slope-intercept form (y = mx + b), which means we need to solve for y: The slope of the line 4x – 5y = –10 is m = 4/5. Therefore, the slope of the line perpendicular to this line would have to be m = –5/4.