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Maths GCSE: Perpendicular Lines on Graphs watch

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    The diagram shows the graph y = 2x + 1.

    A line passes through the point (2, -3) and is perpendicular to y = 2x + 1.

    The equation of this line can be written in the form ax + by = c.

    What are the values a, b and c?

    Please help me! I'm am really, really stuck! All help will be fully appreciated. Would you please include your working out so I can learn from my mistakes! Thank you again
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    Wait the equation is y=-0.5x -2 I think.
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    I have no idea about the values of a, b and c though aha
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    (Original post by acantwellhyde)

    The diagram shows the graph y = 2x + 1.

    A line passes through the point (2, -3) and is perpendicular to y = 2x + 1.

    The equation of this line can be written in form ax + by = c.

    What are the values a, b and c?

    Please help me! I'm am really, really stuck! All help will be fully appreciated. Would you please include your working out so I can learn from my mistakes! Thank you again
    First of all, you need to learn the rules.
    It is against the rules of TSR to give the whole answer out. However, I will obviously help you to get the whole answer yourself, which is what I'm in the process of doing now.

    y = mx + c is the form of a straight line graph, where x is the gradient and c is the y-intercept - where the line passes through the y-axis. To work out the gradient, you use the formula rise/run which is the vertical distance on the y axis / horizontal distance on the x axis. In this case, the question says:
    • The diagram shows the graph y = 2x + 1.
    • A line passes through the point (2, -3) and is perpendicular to y = 2x + 1.
    • The equation of this line can be written in form ax + by = c.
    • What are the values a, b and c?

    This shows that the form is already given, we just need to work out some numbers. The co-ordinates of the other line is (2, -3) and it is perpendicular to the line y = 2x+1. Therefore, the gradient of the new line will be the gradient of - \frac {1}{m}, where m is the gradient of the original line. You can work out the gradient urself using that formula. Now, you can substitute the numbers given (co-ordinates) into the new line and work out y and x and therefore get c. This will give you the whole new equation of the line.
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    (Original post by tabithacrazy)
    Wait the equation is y=-0.5x -2 I think.
    That's correct , if you actually get y and x and substitute them in, the equation would be correct.
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    (Original post by Chittesh14)
    That's correct , if you actually get y and x and substitute them in, the equation would be correct.
    Thanks ps. Was I breaking the rules? I joined tsr a while ago but I just came back on today. If my post was against the rules of tsr I should probably delete it ... X
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    (Original post by tabithacrazy)
    Thanks ps. Was I breaking the rules? I joined tsr a while ago but I just came back on today. If my post was against the rules of tsr I should probably delete it ... X
    It's not really breaking the TSR Rules. But, it gives him a clue to the answer which is fine, it gives half of the answer to him. However, it can help him get the answer easily as he can substitute the values of x and y into the equation and get the full form. It is your choice to delete it :P.
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    (Original post by Chittesh14)
    It's not really breaking the TSR Rules. But, it gives him a clue to the answer which is fine, it gives half of the answer to him. However, it can help him get the answer easily as he can substitute the values of x and y into the equation and get the full form. It is your choice to delete it :P.
    Hi, thanks for your help I think I'll leave it up as it's not giving the full answer however I will be more careful next time and try to just give hints instead
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    (Original post by tabithacrazy)
    Hi, thanks for your help I think I'll leave it up as it's not giving the full answer however I will be more careful next time and try to just give hints instead
    Not a problem, also thanks for giving me a rep. Thought you deserved a rep back for atleast even showing gratitude towards me and the TSR Rules and offering to delete your comment. Thanks for being generous .
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    (Original post by Chittesh14)
    Not a problem, also thanks for giving me a rep. Thought you deserved a rep back for atleast even showing gratitude towards me and the TSR Rules and offering to delete your comment. Thanks for being generous .
    No problem! You deserved it; your maths explanation was really detailed!
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    (Original post by Chittesh14)
    First of all, you need to learn the rules.
    It is against the rules of TSR to give the whole answer out. However, I will obviously help you to get the whole answer yourself, which is what I'm in the process of doing now.

    y = mx + c is the form of a straight line graph, where x is the gradient and c is the y-intercept - where the line passes through the y-axis. To work out the gradient, you use the formula rise/run which is the vertical distance on the y axis / horizontal distance on the x axis. In this case, the question says:
    • The diagram shows the graph y = 2x + 1.
    • A line passes through the point (2, -3) and is perpendicular to y = 2x + 1.
    • The equation of this line can be written in form ax + by = c.
    • What are the values a, b and c?

    This shows that the form is already given, we just need to work out some numbers. The co-ordinates of the other line is (2, -3) and it is perpendicular to the line y = 2x+1. Therefore, the gradient of the new line will be the gradient of - \frac {1}{m}, where m is the gradient of the original line. You can work out the gradient urself using that formula. Now, you can substitute the numbers given (co-ordinates) into the new line and work out y and x and therefore get c. This will give you the whole new equation of the line.
    Thank you so much! This has helped me so much thank you!

    I only signed up to TSR earlier today so I didn't know about that rule. P.S. I'm a girl a = Amelia
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    (Original post by acantwellhyde)
    Thank you so much! This has helped me so much thank you!

    I only signed up to TSR earlier today so I didn't know about that rule. P.S. I'm a girl a = Amelia
    Oh right . Hello Amelia, did you find out the answer to the question, if so what did you get as the answer?
    Also, are you now confident on any questions related to this topic. Would you like me to send you some questions and solutions to questions similar to the one you struggled on, that you've now understood.
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    (Original post by Chittesh14)
    Oh right . Hello Amelia, did you find out the answer to the question, if so what did you get as the answer?
    Also, are you now confident on any questions related to this topic. Would you like me to send you some questions and solutions to questions similar to the one you struggled on, that you've now understood.
    Thank you, with your help I managed to find an answer. Well sort of.



    I did everything you did and found the gradient of the perpendicular line and did the substitution, and in the end I got that the perpendicular line was:

    •y=-1/2x -2 (The slash is a fraction but I didn't know how to type it, sorry!)

    I'm really happy with how I got this and I understand that completely. It was very kind of you to offer to give me some of the questions to help me become more confident with perpendicular lines. Let's just make sure I got this one right first 'ey!

    What I am confused about is that the last part of the question says "the equation of this line can be written in the form ax + by = c." I don't think that y = -1/2x -2 is in that form is it? :confused:

    I know you have helped me already enough, but I was just wondering whether you could tell me what I got is in that form - and if not how do I get it into that form! Thank you so much again!
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    Hello Amelia, well done you've got the answer correct! However, you are correct it is not in the form you wanted it to be. The reason for this is because the form is different for your question, to challenge you. Also, your handwriting is amazing! However, mine is not so it might be a slight struggle reading through the picture.
    The form is ax + by = c.
    Now, we know y = -3, x = 2 and that c = -2.
    a is the number infront of x which is obviously -0.5 in this case. Therefore, ax = (-0.5)2 = -1.
    ax(-1) + by(?) = c(-2)
    Now, -1 + ? = -2. The ? has to be -1.
    Therefore, by has to equal to -1. We already know y = -3. To make by into -1, we have to multiply y by a third, to make it -1. So, by = -1 if b = 1/3. As by will become 1/3 * -3, = -1.
    ax (-1) + by(-1) = c(-2)


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