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basically the reciprocal of the original lines gradient is going to be the gradient for the perpendicular line (remember the signs should switch). For example if i had a line with the gradient of 3, then the gradient of the perpendicular line will be -1over3. But if the line had the gradient of -3, then the line perpendicular to that line will have the gradient 1over3.
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The slope of a line is two-thirds What is the slope of a line that is perpendicular to it?
Perpendicular line = - 1/gradient= - 1/2/3= - 3/2
What is the gradient of a line perpendicular to y equals 4x -2?
6
What is perpendicular to the line 3x plus y equals 2?
If a line has equation y = mx + c, the perpendicular line has gradient -1/m A line perpendicular to 3x + y = 2 has equation 3y = x + c; the value for c will be determined by a point through which the line must pass.
What is the negative reciprocal of a slope?
The negative reciprocal of any gradient gives the gradient of the line perpendicular to it. If you had a line of gradient 2, the negative reciprocal would be -1/2 Just change the sign on the number and flip the number/fraction to get the negative reciprocal.
Write the standard form equation of the line passing through 4 9 and perpendicular to 2x minus 3y equals 7?
With a line in the form y = mx + c, it has gradient m and the line perpendicular to it has gradient m' such that mm' = -1, ie m' = -1/m. A line through a point (x0, y0) with gradient m' has an equation of: y - y0 = m' (x - x0) which can be rearranged to a form for y = mx + c. Thus for the line 2x - 3y = 7: 2x - 3y = 7 → 3y = 2x + 7 → y = 2/3 x + 7/3 → it has gradient 2/3 → perpendicular line has gradient -3/2 → perpendicular line through (4, 9) perpendicular to 2x - 3y = 7 has equation: y - 9 = (-3/2)(x - 4) → 2y - 18 = -3(x - 4) → 2y - 18 = -3x + 12 → 2y = 30 - 3x → 3x + 2y = 30
The slope of a line is two-thirds What is the slope of a line that is perpendicular to it?
Perpendicular line = - 1/gradient= - 1/2/3= - 3/2
What would be the perpendicular line for y equals -x-5?
If the gradient of a line is m, the gradient of a line perpendicular to it (m') is such that mm' = -1, that is: m' = -1/m So for: y = -x - 5 m = -1, so the gradient of a perpendicular line is: m' = -1/-1 = 1 So a general line perpendicular to y = -x - 5 would be: y = x + c A specific line perpendicular to y = -x - 5 at point (xo, -xo-5) on the line is: y - (-xo-5) = 1(x - xo) ⇒ y = x - 2xo - 5
What is the slope of a line perpendicular to the graph of the equation below 2.1x - 5y equals 6.9?
Gradient of given line is 2.1/5 = 21/50 So gradient (slope) of perpendicular is -50/21 = -2.381 (to 3 dp)
Which line is perpendicular to 2x-8y plus 23 equals 0?
4x + y + c = 0 or, for a line going through a given point (xo, yo): y + 4x - (xo + yo) = 0 The gradient of a line multiplied by the gradient of a line perpendicular to it is -1; or in other words: The gradient of the perpendicular line is the negative reciprocal of the gradient of the line. Thus: 2x - 8y + 23 = 0 ⇒ 8y = 2x + 23 ⇒ y = 1/4x + 23/8 ⇒ gradient of perpendicular line is -1 ÷ 1/4 = -4 Thus the equation of the perpendicular line to 2x - 8y + 23 = 0 is 4x + y + c = 0. To find the line through point (xo, yo) perpendicular to 2x - 8y + 23 = 0, use the format: y - yo = m(x - xo) ⇒ y - yo = -4(x - xo) ⇒ y + 4x - (xo + yo) = 0
What is the gradient of a line perpendicular to y equals 4x -2?
6
What is the equation of a line perpendicular to 3x-2y7 with a y- intercept of 5?
The gradient of the given line is 2/3. Gradient of the perpendicular is -3/2 The equation, therefore, is y = -(3/2)x + 5 or 2y = -3x + 10 or 3x + 2y - 10 = 0
What is perpendicular to the line 3x plus y equals 2?
If a line has equation y = mx + c, the perpendicular line has gradient -1/m A line perpendicular to 3x + y = 2 has equation 3y = x + c; the value for c will be determined by a point through which the line must pass.
What is the negative reciprocal of a slope?
The negative reciprocal of any gradient gives the gradient of the line perpendicular to it. If you had a line of gradient 2, the negative reciprocal would be -1/2 Just change the sign on the number and flip the number/fraction to get the negative reciprocal.
How do you name the equation of a line that is perpendicular to y equals 1 half x-3 and goes through the point x equals 0 and y equals 3?
L1: y = 1/2*x - 3Gradient of the line = 1/2Negative reciprocal of gradient = -1/(1/2) = -2That is, gradient of perpendicular = -2.This line goes through (0,3),(y - 3) = 2*(x - 0)y - 3 = 2xy = 2x + 3L1: y = 1/2*x - 3Gradient of the line = 1/2Negative reciprocal of gradient = -1/(1/2) = -2That is, gradient of perpendicular = -2.This line goes through (0,3),(y - 3) = 2*(x - 0)y - 3 = 2xy = 2x + 3L1: y = 1/2*x - 3Gradient of the line = 1/2Negative reciprocal of gradient = -1/(1/2) = -2That is, gradient of perpendicular = -2.This line goes through (0,3),(y - 3) = 2*(x - 0)y - 3 = 2xy = 2x + 3L1: y = 1/2*x - 3Gradient of the line = 1/2Negative reciprocal of gradient = -1/(1/2) = -2That is, gradient of perpendicular = -2.This line goes through (0,3),(y - 3) = 2*(x - 0)y - 3 = 2xy = 2x + 3
What is the slope of the line that is perpendicular to the line whose equation is 2x y 4?
The product of the slope of a line with the slope of a line perpendicular to it is -1.Or to put it another way, if a line has an equationy = mx + ca line perpendicular to it will have a gradient m' such thatmm' = -1⇒ m' = -1/mand an equation ofy = -1/m x + bwhich can be rearranged to givemy + x = d(where d = mb).There are symbols missing from the question, which I suspect are a plus (+) and an equals (=). They can be inserted in two different ways, leading to two different solutions:2x + y = 4⇒ y = -2x + 4 ⇒ gradient of perpendicular line is -1/-2 = 1/2⇒ perpendicular line is:y = 1/2 x + b⇒ 2y = x + c2x = y + 4⇒ y = 2x - 4 ⇒ gradient of perpendicular line is -1/2 = -1/2⇒ perpendicular line is:y = -1/2 x + b⇒ 2y + x = cNote: there is no one perpendicular line, the value of the constant c will vary depending upon what point the line must pass through.
What is the distance from the point 5 7 that is perpendicular to to the straight line equation of 3x-y plus 2 equals 0 on the Cartesian plane showing key aspects of work?
To find the perpendicular distance from a given point to a given line, find the equation of the line perpendicular to the given line which passes through the given point. Then the distance can be calculated as the distance from the given point to the point of intersection of the two lines, which can be calculated by using Pythagoras on the Cartesian coordinates of the two points. A line in the form y = mx + c has gradient m. If a line has gradient m, the line perpendicular to it has gradient m' such that mm' = -1, ie m' = -1/m (the negative reciprocal of the gradient). A line through a point (x0, y0) with gradient m has equation: y - yo = m(x - x0) Thus the equation of the line through (5, 7) that is perpendicular to 3x - y + 2 = 0 can be found. The intercept of this line with 3x - y + 2 = 0 can be calculated as there are now two simultaneous equations. → The perpendicular distance from (5, 7) to the line 3x - y + 2 = 0 is the distance form (5, 7) to this point of interception, calculated via Pythagoras: distance = √((change_in_x)^2 + (change_in_y)^2) This works out to be √10 ≈ 3.162
Write the standard form equation of the line passing through 4 9 and perpendicular to 2x minus 3y equals 7?
With a line in the form y = mx + c, it has gradient m and the line perpendicular to it has gradient m' such that mm' = -1, ie m' = -1/m. A line through a point (x0, y0) with gradient m' has an equation of: y - y0 = m' (x - x0) which can be rearranged to a form for y = mx + c. Thus for the line 2x - 3y = 7: 2x - 3y = 7 → 3y = 2x + 7 → y = 2/3 x + 7/3 → it has gradient 2/3 → perpendicular line has gradient -3/2 → perpendicular line through (4, 9) perpendicular to 2x - 3y = 7 has equation: y - 9 = (-3/2)(x - 4) → 2y - 18 = -3(x - 4) → 2y - 18 = -3x + 12 → 2y = 30 - 3x → 3x + 2y = 30
