When the equation of a line is written in general form, Describe the Slope of the line when A=0 or
and B=0 ?
Thanks!
Ax + By + C = 0
so, the slope is -A/B
take it from there...
When the equation of a line is written in general form as Ax + By = C, where A, B, and C are constants, we can determine the slope of the line by rearranging the equation into slope-intercept form (y = mx + b), where m represents the slope.
To find the slope when A = 0, we substitute 0 for A in the equation Ax + By = C:
0x + By = C
This simplifies to By = C, where B and C are constants.
To isolate y, we divide both sides of the equation by B:
y = C/B
In this case, we can see that the equation does not contain the variable x, meaning the line is a vertical line in which x can take any value but y remains constant. Since the equation does not contain x, the line is parallel to the y-axis. Therefore, the slope of the line when A = 0 is undefined.
To find the slope when B = 0, we substitute 0 for B in the equation Ax + By = C:
Ax + 0y = C
This simplifies to Ax = C, where A and C are constants.
To isolate x, we divide both sides of the equation by A (assuming A is nonzero):
x = C/A
In this case, we can see that the equation does not contain the variable y, meaning the line is a horizontal line in which y can take any value but x remains constant. Since the equation does not contain y, the line is parallel to the x-axis. Therefore, the slope of the line when B = 0 is 0.
To summarize:
- When A = 0, the line is vertical and the slope is undefined.
- When B = 0, the line is horizontal and the slope is 0.