I need help with cartesian planes for my 15 year old

Question

This is a cartesian plane question: Find the equation for the line that is perpendicular to line  y = 2x-3 and passes through the point (1,4)

Answer 1

A perpendicular line has the opposite slope to the given line, which has a slope=2, the x coefficient. The perpendicular slope is -½, because the product of the two slopes has to be -1.

We can use the slope-intercept form of a line to find its equation, plugging in the given point:

y-4=-½(x-1), y=-½x+½+4=-½x+9/2. This can be written in different ways:

2y=9-x, 2y=-x+9, x+2y=9, x+2y-9=0, y=½(9-x). All these are equivalent.

 

Comments

Hi Rod

Thank you very kindly. My son is 14 actually as he reminded me. He is in an elite maths class in his high school, and he doesn't think he should be! We are trying to help and support him but this stuff is a bit over my head.

regards

Danny Hayden

Melbourne, Australia,

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Thanks, Danny, for your appreciation. If George (I guess that’s your son’s name!) needs help on maths, or you yourself need to be enlightened, you can always send me a private message by going to my profile page on this site and clicking on “send private message”. I got to love maths at school mainly because of one particular maths teacher, who fired my enthusiasm. If I can help in any way, I’d be happy to.