Math Is Fun Forum

paulb203

Member

Registered: 2023-02-24

Posts: 345

Straight line graphs

Is the equation for a straight line graph always in the form y=mx+c?

If so, is an equation for a straight line such as y=4 shorthand for y=0x+4?

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Europe2048

Member

Registered: 2024-01-03

Posts: 38

Re: Straight line graphs

Yes, every straight line graph is in the form y=mx+c.

And yes, y=4 is a shorthand for y=0x+4, but I haven't seen something like "y=0x+n" or "y=1x+n" yet.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,820

Re: Straight line graphs

Straight line.

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amnkb

Member

Registered: 2023-09-19

Posts: 253

Re: Straight line graphs

Is the equation for a straight line graph always in the form y=mx+c?

It doesn't have to be; it can be Ax+By+C=0 or other alternates-- but they can all be solved for y= to get y=mx+b

If so, is an equation for a straight line such as y=4 shorthand for y=0x+4?

Exactly-- and writing it your way emphasizes that the slope is zero so the line is horizontal.

paulb203

Member

Registered: 2023-02-24

Posts: 345

Re: Straight line graphs

Thanks, everyone

Regards a straight line being somthing lik, Ax+By+C=0 ; would those kind of equations just be rearrangements of y=mx+c?

I can see that y=mx+c can be rearranged, for example, thus;

m=y-c/(x)

x=y-c/(m)

c=y-mx

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Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Straight line graphs

So substitute A = -m     B = 1     C = -c

Any equation that has x and y and no other variables nor any powers is called a linear equation, because it gives a straight line graph when y is plotted against x.

By using algebraic manipulations the equation can be written in a variety of ways.

If powers are involved the graph will be some sort of curve.

eg

is called a quadratic and the shape is a parabola.

Bob

ps. Your rearrangements need brackets in a different place:

x = (y-c)/m

Subtract c from each side and then divide the whole right hand side by m. As the m is on its own the bracket there adds nothing.

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