the y-intercept of a line through the origin is never, sometimes, or always zero
Isn't y=0 at the origin?
The origin is (0,0)
Both the x and y intercepts at the origin are always 0.
The y-intercept of a line is the point at which the line intersects the y-axis. In general, the y-intercept of a line through the origin (a point with coordinates (0,0)) can be determined by the equation of the line itself.
A line through the origin can be represented by the slope-intercept form, y = mx + b, where m is the slope of the line and b is the y-intercept.
If the line passes through the origin, it means that the y-intercept is the point where x = 0. Plugging x = 0 into the equation of the line gives us y = m(0) + b = 0 + b = b. Therefore, the y-intercept of a line through the origin is always equal to the value of b.
So, the y-intercept of a line through the origin is always zero.
To determine the y-intercept for any line, you can generally follow these steps:
1. Identify the equation of the line, usually given in either slope-intercept form (y = mx + b), point-slope form ((y - y1) = m(x - x1)), or as a general equation (Ax + By = C).
2. Plug in x = 0 into the equation.
3. Solve for y to find the y-intercept.
In the case of a line through the origin, you can directly see that the y-intercept is always zero, without needing to solve any equations.