Graph of ax+by=c: How a,b,c Affects Graph

[sahilmm15]

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

 

[fresh_42]

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?

 

[robphy]

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

 

[Mark44]

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?