what is the equation of a line perpendicular to another?
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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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Correct answer: The slope of this line is 2/3, so the slope of the line perpendicular will have the opposite reciprocal as a slope, which is -3/2.
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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.
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The distance between two points (x_1, y_1) and (x_2, y_2) can be defined as d= \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}. Perpendicular lines are lines that intersect at a 90^{\circ} angle. The product of the slopes of two perpendicular lines is -1.
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Perpendicular Lines and Slopes The slopes of two perpendicular lines are negative reciprocals of each other. This means that if a line is perpendicular to a line that has slope m, then the slope of the line is -1 / m. ... This is why any line that is perpendicular to this line would have slope -2 /1 = -2.
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Step 1: Find the slope of the line. 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 8x + 6y = 15 is m = –4/3. Therefore, the slope of the line perpendicular to this line would have to be m = 3/4.
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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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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.
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Correct answer: The slope of a perpendicular line is the negative reciprocal of the original slope.
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Two lines are perpendicular if and only if they form a right angle. Perpendicular lines always form a right angle of 90º. While perpendicular lines may appear in a slanted or a horizontal position on paper, the lines must always intersect to form a right angle.
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What is the slope of line k? To find the slope of a line perpendicular to a given line, we must take the negative reciprocal of the slope of the given line. Thus the slope of line k is the negative reciprocal of 2/5 (slope of line m), which is -5/2.
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Perpendicular lines are lines that intersect at right angles. If you multiply the slopes of two perpendicular lines in the plane, you get −1 . That is, the slopes of perpendicular lines are opposite reciprocals .
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Perpendicular Lines and Slopes The slopes of two perpendicular lines are negative reciprocals of each other. This means that if a line is perpendicular to a line that has slope m, then the slope of the line is -1 / m. For example, we found that the slope of the line y = (1/2)x + 3 is 1/2.
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Perpendicular lines have opposite reciprocal slopes. Both these lines have reciprocal slopes to the slope of 7 in the original equation, but only the first line is the opposite reciprocal. The correct answer is and .
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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 2 2 . The equation of a perpendicular line to y=2x+4 y = 2 x + 4 must have a slope that is the negative reciprocal of the original slope.
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Distance between Two Parallel Lines It is equal to the length of the perpendicular distance from any point to one of the lines. Let N be the point through which the perpendicular or normal is drawn to l1 from M (− c2/m, 0). We know that the distance between two lines is: d =|Ax1 + By1 + C| / (A2 + B2)½.
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Correct answer: A line perpendicular to another has a slope that is the negative reciprocal of the slope of the other line. The negative reciprocal of the original line is –2, and is thus the slope of its perpendicular line.