if you know that AB=0 and A not=to B, what can you say about the equation Ax+By=1? Describe the graph.
if in Ax + By = 1, AB = 0
then either A =0 or B=0
If A=0, then you have the horizontal line y = 1/B
if B=0, then you have the vertical line x = 1/A
The line above goes through points (-4,-5) and (0,3). What point will the line above go through when y is equal to 8?
You can just look in the back of the textbook, but here is what it says:
The equation will be either
Ax = 1 or By = 1; the graph will be either a vertical or horizontal line.
Here is what I personally wrote:
Either A or B must equal 0, so the equation Ax+By+1 in standard form would either be Ax=1 or By=1. The graph would either be a vertical line or a horizontal line.
OOPS. Sorry I accidentally posted the same thing twice. :D
To understand what can be said about the equation Ax + By = 1 given the information that AB = 0 and A ≠ B, we need to use algebraic reasoning and graphing techniques.
First, since AB = 0 and A ≠ B, we know that either A or B must be equal to 0. Without loss of generality, let's assume B = 0. Therefore, we have AB = 0, which implies A × 0 = 0. Since A ≠ 0, we conclude that 0 = 0, which is true.
Now, let's rewrite the equation Ax + By = 1 by substituting B = 0:
Ax + 0y = 1
Ax = 1
x = 1/A
From this equation, we can observe that the graph of the equation Ax + By = 1 is a vertical line passing through the point (1/A, 0). The reason it is a vertical line is that the coefficient of y is 0.
The graph is independent of the value of A, other than A ≠ 0. Each value of A will result in a different vertical line parallel to the y-axis. The line will intersect the x-axis at the point (1/A, 0).
To summarize, the graph of the equation Ax + By = 1, given AB = 0 and A ≠ B, is a vertical line passing through the point (1/A, 0), where A ≠ 0.