# Graph of ax+by=c

• B
sahilmm15
How does a,b,c effects the equation ax+by=c graphically. Thanks!

Mentor
2022 Award
How does a,b,c effects the equation ax+by=c graphically. Thanks!
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?

Homework Helper
Gold Member
Go to www.desmos.com/calculator/
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

• sahilmm15
Mentor
How does a,b,c effects the equation ax+by=c graphically. Thanks!
If a = 0 and b = 0, the equation is 0x + 0y = c. What can you say about c? Does this equation have any solutions?
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?

• sahilmm15