Is it true that the y-intercept of the straight line with equation Ax + By + C = 0 is -C/B (B �‚ 0).
yes, easy to show
for the y-intercept, x = 0
so in Ax + By + C = 0
0 + By = -C
y = -C/B
btw, what's with the (B,0) thing ?
pretty sure she must have meant B≠0
Yes, it is true that the y-intercept of a straight line with the equation Ax + By + C = 0 is equal to -C/B, given that B ≠ 0.
To understand why this is true, let's break down the equation and discuss the concept of the y-intercept. The equation of a straight line can be written in the slope-intercept form, which is y = mx + b, where m is the slope of the line and b is the y-intercept.
In the given equation Ax + By + C = 0, let's isolate the y term:
By = -Ax - C
Now, divide both sides of the equation by B to solve for y:
y = (-Ax - C) / B
To simplify further, we can distribute the -1/B to each term:
y = -A/B * x - C/B
Comparing this with the slope-intercept form, we can see that the slope of the line is -A/B, and the y-intercept is -C/B. Therefore, the y-intercept is indeed -C/B.
It's important to note that this formula holds true as long as B ≠ 0. If B is equal to zero, the equation Ax + By + C = 0 does not represent a straight line but rather a vertical line parallel to the y-axis. In this case, there is no y-intercept.