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Topic: **How to write an equation perpendicular to a given point****Question:**
I have my Maths GCSE exam on Monday and I'm really stuck on perpendicular lines. I know how to found the negative reciprocal of a perpendicular line but I find the questions about finding the perpendicular line through a given point difficult.
Here's an example on a past paper:
A line has the equation y= - 2x + 3
Write down the equation of the line perpendicular to y= -2 + 3, which goes through the point (0,8).
I'm really not sure how to work it out. Any help is appreciated. Thanks in advance.

November 20, 2019 / By Lavena

Firstly there are two things you must know for this question: the equation of a line: y = mx + c (m = gradient, c = y-intercept or where it crosses the y axis) and that for 2 perpendicular lines, their gradients always multiply to equal -1 ----------------------- So the gradient of y = -2x +3 is -2 Therefore the gradient of the perpendicular line = 1/2 (as -2 * 1/2 = -1) Therefore the equation of the perpendicular line is y = 1/2x + ? We are also given that it goes through the point (0,8) As the x value is 0, this must be the y - intercept - which is therefore 8 Therefore the equation of the perpendicular line is: y = 1/2x + 8 Hope that helps!

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Did you like the answer? We found more questions related to the topic: **How to write an equation perpendicular to a given point**

1) Perpendicular lines have negative inverse slopes, so the slope of the desired line is -5/3. Given the point (3, -6) we can use the formula (y - y1) = m(x - x1) (y - (-6)) = -5/3(x - 3) y + 6 = (-5/3)x + 5 y = (-5/3)x - 1 answer (3) 2) Slope = 1/3 point (3, -1) (y - (-1)) = 1/3(x - 3) y + 1 = (1/3)x - 1 y = (1/3)x - 2 answer (3) or (4) (both are the same) 3) Put the equation into slope-intercept form: 2y + 3x = 6 2y = -3x + 6 y = (-3/2)x + 3 slope is -3/2 so perpendicular line will have slope of 2/3 m = 2/3, point(6, 5) (y - 5) = 2/3(x - 6) y - 5 = (2/3)x - 4 y = (2/3)x + 1 4) Parallel lines have the same slope. 2y + 3x = 8 2y = -3x + 8 y = (-3/2)x + 4 m= -3/2 point (2, -1) (y - (-1)) = -3/2(x - 2) y + 1 = (-3/2)x + 3 y = (-3/2)x + 2 answer (4) 5) 2x - 3y = 11 -3y = -2x + 11 y = (2/3)x - 11/3 m = 2/3 point (6, -5) (y - (-5)) = 2/3(x - 6) y + 5 = (2/3)x - 4 - .--

a) come across the slope of y = x-6 y = mx + b => m = a million so the slope of the line = a million come across the intercept (b) replace the normally taking place element => 2 = a million*(-a million) + b 2 = -a million +b 3 = b So the equation is y = 1x + 3 b) for a perpendicular line, you know that the slope is the detrimental id of the quite a few line y = -x => m = -a million so the perpindicular line could have a slope of m = a million 2 = a million*(a million) + b 2 = a million + b b = a million y = 1x + a million

so the line is y = -2x +3 which makes the gradient -2. the gradient of the perpendicular is 1/2 using what i named the 'crossing over' method, (y-8)/(x-0)=1/2 if it goes through the point,say (12,9) the eqn would be (y-9)/(x-12)=1/2 the answer in this case is 2y= x + 16 good luck for your GCSE! i just took mine. :)

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The common solution to write this equation is y = mx + b or y = -3x + one million The slope of the given line = -three The slope of the perpendicular is one million/-slope of the given line = one million/-(-three) = one million/three So a long way what we've got for the perpendicular is y = one million/three x + b Now we all know that this line have to pass by way of (6,three) so three = one million/three * 6 + b three = two + b b = three - two = one million The slope of the preferred line is y = one million/three (x) + one million

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So you know what the term "negative reciprocal" is? It's what you use to figure out the sloe of a perpendicular line. A negative reciprocal is when you flip the numerator and denominator, and then you add a negative sign in front of it. A reciprocal is the number that makes a product of 1 from the original number. For example, 3/4 and 4/3 are reciprocals because if you multiply them together, you get 1. QUESTION: Let's give an example. Find a line perpendicular to y= 1/2x+2 that passes through the point (4,-4) So you find the negative reciprocal of 1/2 (the slope of the line) that is, you find the opposite of this number (by adding a negative sign), then flip the numerator and denominator (to get the reciprocal). so you get -2 as the slope of your perpendicular line. Let's use the slope-intercept form. y=ax+b a is slope and b is the y intercept. so you got this equation y=-2x+b Now, you need to find b, to get the equation of a line. Since the line passes through the point (4, -4), you SUBSTITUTE these numbers into the equation. Since the coordinates are (x,y), x=4 and y=-4. Then you insert into your equation. -4= -2(4)+b Simplify, then you should get b=4 that means the b in the equation is 4. so the line is y= -2x+4 This is just an example. Hope it helped!

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