- #1

sahilmm15

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How does a,b,c effects the equation ax+by=c graphically. Thanks!

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- Thread starter sahilmm15
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- #1

sahilmm15

- 100

- 27

How does a,b,c effects the equation ax+by=c graphically. Thanks!

- #2

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Write it as ##\begin{bmatrix} a & b \end{bmatrix} \cdot \begin{bmatrix} x \\ y \end{bmatrix}=c ## and ask again. What does ##c=0 ## and ##c\neq 0## mean, and what stands ##(a,b)## for?How does a,b,c effects the equation ax+by=c graphically. Thanks!

- #3

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Type in

ax+by=c

ax=c

by=c

(a,b)

y=(b/a)x

Find the x-coordinate of the intersection

by plugging in the last equation into the first equation and solve for x.

Solve the y=(b/a)x for x.

Plug that new equation into the first equation and solve for y

How far is that point from the origin? Call it d.

Enter another equation

r=d

- #4

Mark44

Mentor

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If a = 0 and b = 0, the equation is 0x + 0y = c. What can you say about c? Does this equation have any solutions?How does a,b,c effects the equation ax+by=c graphically. Thanks!

If b = 0, and ##a \ne 0##, the equation is ax = c, or ##x = \frac c a##. What does the graph of this equation look like?

If a = 0 and ##b \ne 0##, the equation is by = c, or ##y = \frac c b##. What does the graph of this equation look like?

If ##a \ne 0## and ##b \ne 0## solve for y in terms of x and the constant c. What does the graph of this equation look like?

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