explain to me why the first coordinate of the y intercept is always 0 please.
The y-intercept, by definition, lies on the y-axis
Any point on the y-axis has an x value of 0
(you haven't gone either left or right from the origin)
The y-intercept is the point where a line crosses the y-axis, which is the vertical axis on a coordinate plane. The coordinates of any point on the y-axis have an x-coordinate of 0.
To understand why the first coordinate of the y-intercept is always 0, consider the equation of a line in slope-intercept form: y = mx + b. In this equation, 'y' represents the y-coordinate, 'x' represents the x-coordinate, 'm' represents the slope of the line, and 'b' represents the y-intercept.
When a line crosses the y-axis, the x-coordinate of that point is always 0 because it lies directly on the vertical line. Plugging in x = 0 into the equation, it becomes y = m(0) + b, which simplifies to y = b. This means that the value of y at the y-intercept is simply equal to the value of b. Therefore, the first coordinate of the y-intercept is always 0.
To understand why the first coordinate of the y-intercept is always 0, let's first clarify what the y-intercept is. In a Cartesian coordinate system, the y-intercept is the point where a function or a graph crosses the y-axis.
The y-axis is a vertical line that runs through the origin, which is the point where the x-axis and y-axis meet. The x-coordinate of the origin is 0, and the y-coordinate can be any value along the y-axis.
When a graph or function intersects the y-axis, this means the x-coordinate of that point is 0. Therefore, for the y-intercept, the first coordinate (x-coordinate) is always 0.
For example, in the equation of a straight line y = mx + b, where m represents the slope of the line and b represents the y-intercept, the first coordinate of the y-intercept is always 0 because it corresponds to the point where the line crosses the y-axis.
To find the y-intercept of a graph or a function, you can set the x-coordinate to 0 and solve for the corresponding y-coordinate. This will give you the point where the graph or function crosses the y-axis.