I need help understanding this and possibly how to do it...
For the equation Ax + By = C (where A, B, C are real numbers) what is the slope (in terms of the traditional y = mx+ b) and state any restrictions.
Yeah, same here
So let's just change Ax + By = C to the form y = mx + b
Ax + By = C
By = -Ax + C
divide each term by B
y = (-A/B)x + C/B
So compare that to y = mx + b
m = -A/B
so I have just developed a quick way to find the slope of any equation in general form
e.g. 7x + 9y = 17
has slpe -A/B = -7/9
e.g. 3x - 5y = 19
slope = -3/-5 = 3/5
Thanks Reiny!! I understand now ! haha
To find the slope of the equation Ax + By = C in the form of y = mx + b, we need to manipulate the given equation to isolate y. Here's how you can do it:
Step 1: Start with the equation Ax + By = C.
Step 2: Subtract Ax from both sides to isolate By. This gives us By = -Ax + C.
Step 3: Divide both sides by B to solve for y. This gives us y = (-A/B)x + (C/B).
Now we can determine the slope (m) of the equation. Comparing the equation to the standard form of y = mx + b, we can see that the coefficient of x, (-A/B), is the slope of the line.
So, in terms of y = mx + b, the slope is -A/B.
As for restrictions, there are none for finding the slope. However, there may be restrictions on the values of A and B or any other variables used in the equation, depending on the context or specific problem.